Free Sequences and Series MCQs with Answers
163 Sequences and Series MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Sequences describe ordered terms formed by a pattern, while series represent the sum of those terms. Questions cover arithmetic and geometric sequences, their nth terms, common difference or ratio, finite sums, and applications, with the sequence itself kept distinct from the corresponding series.
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163 questions · page 8 of 9
- A. n
- B. n + 1
- C. 2^n
- D. 2^n - 1
Explanation: The number of terms in the expansion of (a + b)^n is given by the formula:2^nWhere n is the exponent of the binomial expression
Correct answer: 2^n- A. n
- B. n - 1
- C. n + 1
- D. 2n
Explanation: The general term of the binomial expansion (a + x)^n is given by the formula:(n choose r) a^(n-r) x^rWhere:n is the exponent of the…
Correct answer: 2n- A. (n choose r+1) a^(n-r-1) x^r
- B. (n choose r) a^(n-r) x^r
- C. (n choose r-1) a^(n-r+1) x^r+1
- D. (n choose r) a^(n-r+1) x^r+1
Explanation: The general term of the binomial expansion (a + x)^n is given by the formula:(n choose r) a^(n-r) x^rWhere:n is the exponent of the…
Correct answer: (n choose r) a^(n-r+1) x^r+1- A. decreases from n to 0
- B. increases from 0 to n
- C. remains n everywhere
- D. becomes n at the end
Explanation: In the expansion of (a + x)^n, the general term is given by:(n choose r) a^(n-r) x^rWhere:n is the exponent of the binomial expressionr is…
Correct answer: decreases from n to 0- A. decreases from n to 0
- B. Increases from 0 to n
- C. remains n everywhere
- D. becomes 0 at the end
Explanation: In the expansion of (a + x)^n, the general term is given by:(n choose r) a^(n-r) x^rWhere:n is the exponent of the binomial expressionr is…
Correct answer: Increases from 0 to n- A. T7
- B. T8
- C. T6 & T7
- D. T7 & T8
Explanation: Since the exponent n = 14, which is an even number, the middle term will be a single term.The middle term in the expansion of (a - 3x)^n…
Correct answer: T8- A. 18
- B. 20
- C. 21
- D. 19
Explanation: In the expansion of (a + b)^n, the number of terms is n+1.This is because the index r in the general term (n choose r) a^(n-r) b^r ranges…
Correct answer: 21- A. n
- B. n/2
- C. n - 1
- D. n + 1
Explanation: In the expansion of (a + b)^n, the number of terms is n + 1.This is because the index r in the general term (n choose r) a^(n-r) b^r…
Correct answer: n + 1- A. odd
- B. even
- C. prime
- D. none of these
Explanation: The middle term in the expansion of (a + b)^n, where n is an even number, is an even term.The general term in the expansion is given by:(n…
Correct answer: even- A. |x| < 1/4
- B. |x| > 1/4
- C. -1 ≤ x < 1
- D. |x| ≤ -1
Explanation: The binomial expansion (1 - 4x)^2 is valid when the absolute value of the ratio of the second term to the first term is less than 1.In…
Correct answer: |x| < 1/4- A. n ≥ 3
- B. n ≥ 1
- C. n ≥ 2
- D. n ≥ -1
Explanation: To determine the range of values for n where n^2 > n + 3 is true, we need to solve the inequality:n^2 > n + 3Rearranging the inequality…
Correct answer: n ≥ 3- A. 1
- B. 0
- C. 2n
- D. n
Explanation: The general term in the binomial expansion (a + b)^n is given by:(n choose r) a^(n-r) b^rThe sum of the exponents of a and b in each term…
Correct answer: n- A. |x| < 0
- B. |x| < 1/2
- C. |x| < 2
- D. |x| < 1
Explanation: The binomial expansion (1-2x)^-2 is valid when the absolute value of the ratio of the second term to the first term is less than 1.In this…
Correct answer: |x| < 1/2- A. First
- B. Second
- C. Middle
- D. Last
Explanation: The expansion of (x + 2)^8 can be written as:(x + 2)^8 = x^8 + 8x^7(2) + 28x^6(2)^2 + 56x^5(2)^3 + 70x^4(2)^4 + 56x^3(2)^5 + 28x^2(2)^6 +…
Correct answer: Last- A. (n+1)/2
- B. (n+3)/2
- C. (n-1)/2
- D. (n+1)/2 and (n+3)/2
Explanation: When n is an odd number, the expansion of (a + x)^n has two middle terms.The general term in the expansion of (a + x)^n is given by:(n…
Correct answer: (n+1)/2 and (n+3)/2- A. x ≤ 1
- B. -1 ≤ x < 1
- C. x > 1
- D. x =1
Explanation: The binomial series (1+x)^n is defined and convergent when the value of x lies between -1 and 1, i.e., -1 ≤ x < 1.When x is greater than…
Correct answer: -1 ≤ x < 1- A. 23
- B. 64
- C. 128
- D. 256
Explanation: Correct answer is"c. 128"To find the sum of the coefficients of the odd powers of \( x \) in the expansion of \( (1 + x)^n \), where \( n…
Correct answer: 128- A. 30
- B. 31
- C. 32
- D. None of these
Explanation: The correct answer is c) 32.The expansion of (x + y)^5 can be written as:(x + y)^5 = x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5The…
Correct answer: 32- A. 494
- B. 495
- C. 496
- D. 497
Explanation: The correct answer is b) 495.The general term of the binomial expansion of (a + x)^r is given as:Tr+1 = (r!(a)^(r-r)(x)^rThe given…
Correct answer: 495- A. 540x^3
- B. -22680x^3
- C. 1040x^4
- D. None of these
Explanation: The correct answer is b) -22680x^3.The expansion of (3 - 2x)^7 can be written as:(3 - 2x)^7 = 3^7 - 7(3)^6(-2x) + 21(3)^5(-2x)^2 -…
Correct answer: -22680x^3