MCQ Test- Sequence and series (Class- 9, Experience- 2)

• Topics
• MCQ Test
• Exercise Solution

Multiple Choice Quiz: Test Your Knowledge!

Question 1: What can the number of terms in a sequence be?

A. Only finite
B. Only infinite
C. Both finite and infinite
D. None of the above

Question 2: What is a sequence with a specified number of terms called?

A. Infinite sequence
B. Finite sequence
C. Arithmetic sequence
D. Geometric sequence

Question 3: What is an arithmetic sequence?

A. A sequence where the ratio between terms is constant
B. A sequence where the difference between terms is constant
C. A sequence that follows the Fibonacci pattern
D. A sequence that is infinite

Question 4: What is a geometric sequence?

A. A sequence where the ratio between terms is constant
B. A sequence where the difference between terms is constant
C. A sequence that follows the Fibonacci pattern
D. A sequence that is finite

Question 5: What did Leonardo Pisano discover by searching nature?

A. Arithmetic sequence
B. Geometric sequence
C. Fibonacci sequence
D. Harmonic sequence

Question 6: How is the Fibonacci sequence different from arithmetic and geometric sequences?

A. It is a finite sequence
B. It is an infinite sequence
C. Each term is the sum of the previous two terms
D. Each term is the product of the previous two terms

Question 7: What is the relation of the set of real numbers to another collection called?

A. series
B. set
C. function
D. sequence

Question 8: What is the general rule of the Fibonacci sequence?

A. Each term is double the previous term
B. Each term is the sum of the previous two terms
C. Each term is triple the previous term
D. Each term is the product of the previous two terms

Question 9: What are the first 10 terms of the Fibonacci sequence?

A. 0,1,1,2,3,5,8,13,21,34
B. 1,1,2,3,5,8,13,21,34,55
C. 0,1,2,3,5,8,13,21,34,55
D. 1,2,3,5,8,13,21,34,55,89

Question 10: What can be the number of terms in a sequence?

A. only finite
B. only infinite
C. Both finite and infinite
D. None of the above

Question 11: What is a sequence with an unspecified number of terms called?

A. Infinite sequence
B. Finite sequence
C. Arithmetic sequence
D. Geometric sequence

Question 12: In an arithmetic sequence, what is the relation between terms?

A. The terms are multiplied by a specific number
B. The terms are added or subtracted by a specific number
C. The terms follow a specific ratio
D. The terms are squares of natural numbers

Question 13: What is a sequence called where the ratio of any term to its previous term is constant?

A. Arithmetic sequence
B. Geometric sequence
C. Fibonacci sequence
D. Finite sequence

Question 14: Who discovered the Fibonacci sequence?

A. Carl Friedrich Gauss
B. Leonardo Pisano
C. Pythagoras
D. Charls David

Question 15: What is the first term of the Fibonacci sequence?

A. 0
B. 1
C. 2
D. 3

Question 16: What is the second term of the Fibonacci sequence?

A. 0
B. 1
C. 2
D. 3

Question 17: In which book was the Fibonacci sequence published?

A. Principia Mathematica
B. Liber Abaci
C. Elements
D. The Art of Computer Programming

Question 18: If the terms of a sequence are joined by a (+) sign, what is obtained?

A. Sequence
B. Series
C. Function
D. Set

Question 19: What is a series with a definite number of terms called?

A. Infinite series
B. Finite series
C. Arithmetic series
D. Geometric series

Question 20: What is a series with an indefinite number of terms called?

A. Infinite series
B. Finite series
C. Arithmetic series
D. Geometric series

Question 21: What pattern did Fibonacci discover?

A. Arithmetic sequence
B. Geometric sequence
C. Fibonacci sequence
D. Harmonic sequence

Question 22: What is the common difference in an arithmetic sequence?

A. The product of terms
B. The sum of terms
C. The difference between consecutive terms
D. The ratio of consecutive terms

Question 23: What is the common ratio in a geometric sequence?

A. The product of terms
B. The sum of terms
C. The difference between consecutive terms
D. The ratio of consecutive terms

Question 24: Who is credited with the Fibonacci sequence's discovery in the provided text?

A. Carl Friedrich Gauss
B. Isaac Newton
C. Leonardo Pisano
D. Albert Einstein

Question 25: What does the term "finite" indicate about a sequence?

A. It has a specified number of terms
B. It has an unspecified number of terms
C. It is an arithmetic sequence
D. It is a geometric sequence

Question 26: What mathematical concept did Carl Friedrich Gauss help to determine?

A. The Fibonacci sequence
B. The sum of the first series
C. The common difference in arithmetic sequences
D. The common ratio in geometric sequences

Question 27: How is a finite series different from an infinite series?

A. A finite series has a limited number of terms
B. A finite series has an unlimited number of terms
C. A finite series follows a common ratio
D. A finite series follows a common difference

Question 28: What does the ratio between any term and its preceding term represent in a geometric sequence?

A. The sum of terms
B. The product of terms
C. A specific constant number
D. The difference between terms

Question 29: Which mathematician's nickname was Fibonacci?

A. Carl Friedrich Gauss
B. Leonardo Pisano
C. Euclid
D. Pythagoras

Question 30: What type of sequence adds or subtracts a specific number to/from the preceding term?

A. Arithmetic sequence
B. Geometric sequence
C. Fibonacci sequence
D. Harmonic sequence

Question 31: What does an infinite sequence imply?

A. It has a specific ending
B. It has no ending
C. It has a finite number of terms
D. It is an arithmetic sequence

Question 32: What book did Leonardo Pisano publish his findings in?

A. The Art of Computer Programming
B. Liber Abaci
C. Principia Mathematica
D. Elements

Question 33: What term is used for a series if its number of terms is definite?

A. Infinite series
B. Finite series
C. Arithmetic series
D. Geometric series

Question 34: Which mathematician is known for the method to determine the sum of series?

A. Leonardo Pisano
B. Carl Friedrich Gauss
C. Isaac Newton
D. Pythagoras

Question 35: What is the first term in the Fibonacci sequence?

A. 1
B. 0
C. 2
D. 3

Question 36: What does the term "arithmetic sequence" refer to?

A. A sequence where the ratio between terms is constant
B. A sequence where the difference between terms is constant
C. A sequence that follows the Fibonacci pattern
D. A sequence that is finite

Question 37: What property does a geometric sequence follow?

A. The difference between terms is constant
B. The ratio between terms is constant
C. The sum of terms is constant
D. The product of terms is constant

Question 38: What pattern is followed in a Fibonacci sequence?

A. Each term is the sum of the previous two terms
B. Each term is the difference of the previous two terms
C. Each term is the product of the previous two terms
D. Each term is the ratio of the previous two terms

Question 39: What type of sequence is described by the ratio of any term to its previous term being constant?

A. Arithmetic sequence
B. Geometric sequence
C. Fibonacci sequence
D. Harmonic sequence

Question 40: What does a finite sequence have that an infinite sequence does not?

A. A common ratio
B. A specified number of terms
C. An unspecified number of terms
D. A common difference

Question 41: In what context is Carl Friedrich Gauss mentioned?

A. For discovering the Fibonacci sequence
B. For determining the sum of series
C. For inventing the geometric sequence
D. For writing Liber Abaci

Question 42: What does the Fibonacci sequence start with?

A. 1 and 1
B. 0 and 1
C. 1 and 2
D. 0 and 2

Question 43: What kind of sequence is formed by adding or subtracting a specific number to/from the preceding term?

A. Arithmetic sequence
B. Geometric sequence
C. Fibonacci sequence
D. Infinite sequence

Question 44: What sequence has a specified number of terms and an ending?

A. Finite sequence
B. Infinite sequence
C. Arithmetic sequence
D. Geometric sequence

Question 45: What sequence has an unspecified number of terms and no ending?

A. Finite sequence
B. Infinite sequence
C. Arithmetic sequence
D. Geometric sequence

Question 46: How did Fibonacci discover the sequence named after him?

A. By studying arithmetic sequences
B. By searching nature
C. By analyzing geometric sequences
D. By writing a mathematical proof

Question 47: Which book did Fibonacci's sequence appear in?

A. Liber Abaci
B. Elements
C. Principia Mathematica
D. The Art of Computer Programming

Question 48: Who developed the method for determining the sum of series?

A. Leonardo Pisano
B. Carl Friedrich Gauss
C. Euclid
D. Pythagoras

Question 49: What is a sequence with a fixed number of terms called?

A. infinite sequence
B. finite sequence
C. arithmetic sequence
D. geometric sequence

Question 50: What is the common difference of a finite arithmetic sequence 2,5,8,11,14?

A. 5
B. 2
C. 3
D. 4

Question 51: What is the common ratio of a finite geometric section 3,6,12,24?

A. 1
B. 2
C. 3
D. 4

Question 52: The first term of an series is 5 and the difference is 3. What is the fifth term of the clause?

A. 15
B. 17
C. 18
D. 20

Question 53: What is a sequence with indefinite number of terms called?

A. arithmetic sequence
B. geometric sequence
C. infinite sequence
D. finite sequence

Question 54: In a arithmetic Sequence, what is the relationship between the terms?

A. The terms are multiplied by a certain number
B. Terms are added or subtracted to a certain number
C. The terms follow a certain ratio
D. The terms are the square of the real number

Question 55: In which sequence, the ratio of the previous term to the next term is a fixed number?

A. arithmetic sequence
B. geometric sequence
C. Fibonacci sequence
D. finite sequence

Question 56: What is the first term of Fibonacci sequence?

A. 0
B. 1
C. 2
D. 3

Question 57: What is the second term of Fibonacci sequence?

A. 0
B. 1
C. 2
D. 3

Question 58: What is obtained when the terms of a sequence are added by (+) sign?

A. sequence
B. series
C. function
D. set

Question 59: What is an series with a fixed number of terms called?

A. Infinite series
B. Finite series
C. arithmetic flow
D. Geometric series

Question 60: Which pattern was discovered by Fibonacci?

A. arithmetic sequence
B. geometric sequence
C. Fibonacci sequence
D. Harmonic sequence

Question 61: What is the common difference of a arithmetic Sequence?

A. Product of terms
B. sum of terms
C. Difference between the following terms
D. Ratio of next terms

Question 62: What is the common ratio of a geometric sequence?

A. Product of terms
B. sum of terms
C. Difference between the following terms
D. Ratio of next terms

Question 63: Who is credited with discovering the Fibonacci sequence?

A. Carl Friedrich Gauss
B. Isaac Newton
C. Leonardo Pisano
D. Albert Einstein

Question 64: What does the term finite indicate about a sequence?

A. It has a certain number of terms
B. It has an indefinite number of terms
C. This is a arithmetic sequence
D. This is a geometric sequence

Question 65: What math did Carl Friedrich Gauss help determine the solution to?

A. Fibonacci sequence
B. The first term is the sum
C. Common differences of arithmetic sequences
D. Common ratio of exponential sequence

Question 66: How does a finite clause differ from an infinite clause?

A. The number of terms in a finite sequence is limited
B. The number of terms in a finite sequence is unlimited
C. A finite series follows a common ratio
D. A finite series follows a common difference

Question 67: What does the ratio of the previous term to the next term in the geometric Sequence indicate?

A. sum of terms
B. Product of terms
C. A certain fixed number
D. Difference of terms

Question 68: Which mathematician was nicknamed Fibonacci?

A. Carl Friedrich Gauss
B. Leonardo Pisano
C. Euclid
D. Pythagoras

Question 69: In which sequence is a certain number added or subtracted to the previous term?

A. arithmetic sequence
B. geometric sequence
C. Fibonacci sequence
D. Harmonic sequence

Question 70: What does an infinite sequence indicate?

A. It has a definite ending
B. It has no end
C. It has a finite number of positions
D. This is a arithmetic sequence

Question 71: In which book did Leonardo Pisano publish his research?

A. The Art of Computer Programming
B. Liber Abachi
C. Principia Mathematica
D. elements

Question 72: What is the clause called if the number of terms is fixed?

A. Infinite series
B. Finite series
C. arithmetic series
D. Geometric series

Question 73: Which mathematician developed the method of determining sum of series?

A. Leonardo Pisano
B. Euclid
C. Pythagoras
D. Carl Friedrich Gauss

Question 74: What does the term arithmetic Sequence refer to?

A. A sequence in which the ratio of terms is constant
B. A sequence in which the difference between the terms is constant
C. A sequence that follows the Fibonacci pattern
D. is a finite sequence

Question 75: Which property follows the geometric Sequence?

A. The difference between the terms remains constant
B. The ratio of the terms remains constant
C. The sum of the terms remains constant
D. The product of the terms remains constant

Question 76: What pattern does the Fibonacci sequence follow?

A. Each term is the sum of the previous two terms
B. Each term is the difference of the previous two terms
C. Each term is the product of the previous two terms
D. Each term is the ratio of the previous two terms

Question 77: In which type of sequence is the ratio of the previous term to the next term constant?

A. arithmetic sequence
B. geometric sequence
C. Fibonacci sequence
D. Harmonic sequence

Question 78: What type of sequence is formed by adding or subtracting a fixed number to the previous term?

A. arithmetic sequence
B. geometric sequence
C. Fibonacci sequence
D. infinite sequence

Question 79: Which sequence has a fixed number of terms and an ending?

A. finite sequence
B. infinite sequence
C. arithmetic sequence
D. geometric sequence

Question 80: Which sequence has an indefinite number of terms and no termination?

A. finite sequence
B. infinite sequence
C. arithmetic sequence
D. geometric sequence

Question 81: How did Fibonacci discover a sequence named after him?

A. By studying arithmetic sequences
B. By geometric sequence analysis
C. Write a arithmetic proof
D. Nature investigates

Question 82: Who developed the method of determining sum of lines?

A. Leonardo Pisano
B. Carl Friedrich Gauss
C. Euclid
D. Pythagoras

Question 83: What is a arithmetic Sequence?

A. A sequence in which the ratio of terms is constant
B. A sequence in which the difference between the terms is constant
C. A sequence that follows the Fibonacci pattern
D. is a finite sequence

Question 84: What did Leonardo Pisano discover by exploring nature?

A. arithmetic sequence
B. geometric sequence
C. Fibonacci sequence
D. Harmonic sequence

Question 85: How does the Fibonacci sequence differ from parallel and geometric sequences?

A. It is a finite sequence
B. It is an infinite sequence
C. Each term is the sum of the previous two terms
D. Each term is the product of the previous two terms

Question 86: What is the formula for finding the sum of a finite arithmetic series?

A. S_n = n2(a + l)
B. S_n = n2[2a + (n - 1)d]
C. S_n = a + (n - 1)d
D. S_n = a + l   2

Question 87: What is the condition for determining the sum of a infinite series of geometric series?

A. ∣r∣ ＞ 1
B. r = 1
C. r = -1
D. ∣r∣ ＜ 1

Question 88: How is the Common Difference of an Arithmetic Sequence determined?

A. d = a_n + a_n-1
B. d = a_n - a_n-1
C. d =  a_na_n-1
D. d = a_n-1 - a_n

Question 89: How is the common ratio of a geometric sequence determined?

A. r =  a_na_n-1
B. r = a_n - a_n-1
C. r = a_n-1 - a_n
D. r =  a_n-1  a_n

Question 90: What is the formula for determining the nth term (n-th term) of an arithmetic expression?

A. a_n = a⋅r^n-1
B. a_n = a + 1   2
C. a_n = n2(a + l)
D. a_n = a + (n - 1)d

Question 91: What is the formula for determining the n-th term of a geometric series?

A. a_n = a + (n - 1)d
B. a_n = a⋅r^n-1
C. a_n = a + 1   2
D. a_n = n2(a + l)

Question 92: 5th value is 243 and 1st value is 3 of a geometric series. What is the common ratio of the series?

A. 5
B. 2
C. 4
D. 3

Question 93: The 10th term of a numerator is 30, and the first term is 3. What is the common difference between the series?

A. 2.7
B. 3
C. 3.3
D. 5

Question 94: If the common ratio of a geometric series is r= 0.50 and the first term is 8, what is the sixth term of the series?

A. 0.5
B. 0.25
C. 0.125
D. 0.0625

Question 95: The first term of a geometric series is a=10 and the common ratio is r=-2. What is the fourth term of the clause?

A. 80
B. -80
C. 40
D. -40

Question 96: What is the formula for finding nth term of Fibonacci sequence?

A. F_n = F_n-1 + F_n-2
B. F_n = F_n-1 × F_n-2
C. F_n = F_n-1 - F_n-2
D. F_n = 2 × F_n-1

Question 97: What is the seventh term of the Fibonacci sequence?

A. 8
B. 13
C. 21
D. 34

Question 98: 1+2+3+4+...+n What is the formula to find the sum of this series?

A. n²
B. n(n - 1)
C. n(n + 1)    2
D. n(n - 1)    2

Question 99: 1²+2²+3²+...+n² What is the formula to find the sum of this expression ?

A. n(n + 1)       2
B. n(n + 1) (2n + 1)           6
C. n(n - 1) (2n - 1)          6
D. n(n + 1)(2n + 1)

Question 100: 1+3+5+7+...+(2n-1) What is the sum of this sequence?

A. n²
B. n(n+1)
C. n(n + 1)(2n + 1)
D. 2n

Question 101: The first term of an infinite geometric series is 2 and the common ratio is 0.5. What is the sum of this clause?

A. 3
B. 4
C. 5
D. 6

Question 102: The first term of a geometric series is 3 and the common ratio is 2. What will be the fourth term of the clause?

A. 24
B. 30
C. 36
D. 48

Question 103: 5,25,125,625,... What is the common ratio of this geometric series?

A. 15
B. 25
C. 10
D. 5

Question 104: What is a hierarchy?

A. An array of numbers or objects
B. sum of numbers
C. A circle of numbers or objects
D. A set of numbers arranged according to a certain rule

Question 105: 1,4,9,16,... What is the name of this sequence?

A. Natural number sequence
B. geometric sequence
C. Square number sequence
D. arithmetic sequence

Question 106: What is a series?

A. sum of numbers
B. An array of numbers or objects
C. Product of numbers
D. difference of numbers

Question 107: 2+4+6+8+... What is the name of this series?

A. geometric series
B. arithmetic flow
C. square number series
D. Prime number series

Question 108: What are the characteristics of a arithmetic Sequence?

A. Each term is double the previous term
B. Each term is obtained by adding a certain number to the previous term
C. Each term is obtained by multiplying the previous term by a certain number
D. Each term is the sum of the previous two terms

Question 109: 6.3,7,11,15,... What is the common interval of this arithmetic Sequence?

A. 2
B. 3
C. 4
D. 5

Question 110: What are the characteristics of a geometric Sequence?

A. Each term is a fixed number with the preceding term
B. Each term is obtained by multiplying the previous term by a certain number
C. Each term is the sum of the previous two terms
D. Each term is obtained by dividing a certain number by the previous term

Question 111: 8.5,15,45,135,... What is the common ratio of this geometric sequence?

A. 2
B. 3
C. 4
D. 5

Question 112: 1,1,2,3,5,8,... What is the name of this sequence?

A. arithmetic sequence
B. geometric sequence
C. Fibonacci sequence
D. Prime number sequence

Question 113: 12, 14, 18,  110 ... এই অনুক্রমটির সাধারণ অনুপাত কী?

A. 12
B. 14
C. 18
D.  116