68 free MCQs on Sequences and Series, each with its own worked answer and explanation. Arithmetic progressions, geometric progressions, and sums
Take the timed Sequences and Series chapterwise test →68 practice questions on Sequences and Series, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Sequences and Series notes.
Bar heights for AP 2, 5, 8, 11 with the common difference d=3 marked between consecutive terms.
Q1.
In an AP, the common difference d between 2, 5, 8, 11,... is:
Q3.
What is the nth term formula for an AP?
Q4.
Sum of first n terms of an AP with first term a and last term l:
Q9.
Sum of first n squares: 1² + 2² + 3² + ... + n² =
Q10.
The sequence 1, 4, 9, 16,... is:
Q12.
The sum to infinity of a GP with first term 1 and r = 1/2 is:
Q13.
Sum of first n odd numbers (1+3+5+...+(2n-1)) =
Q21.
Find the sum of first 20 terms of AP: 1, 4, 7,...
Q22.
How many terms of AP: 18, 16, 14,... are needed for sum = 0?
Q23.
In a GP, the 3rd term is 24 and the 6th is 192. Find the common ratio.
Q25.
Insert 3 arithmetic means between 5 and 21.
Q27.
Three numbers in AP have sum 24 and product 440. Find them.
Q29.
The 7th term of GP is 192 and common ratio is 2. Find the first term.
Q30.
Sum of first n terms of GP: 1, -1, 1, -1,... when n is even is:
Q31.
Sum of cubes: 1³ + 2³ + 3³ + ... + n³ =
Q32.
If AM = 25 and GM = 20, find the two numbers.
Q33.
In an AP, the p-th term is q and q-th term is p. The (p+q)-th term is:
Q34.
If the sum of an infinite GP is 3 and sum of squares of its terms is 9/5, find the series.
Q35.
The 4th term of a GP is 250 and the ratio is 5. First term is:
Q36.
Sum of AP: a + (a+d) + (a+2d) + ... to n terms when a = 3, d = 2, n = 12:
Q37.
In an AP, if Sn = 3n² + 5n, find the nth term.
Q38.
A ball dropped from 10 m bounces 3/5 of previous height. Total distance travelled:
Q40.
The sum 1/(1×2) + 1/(2×3) + 1/(3×4) + ... to n terms =
Q41.
Sum: 1×2 + 2×3 + 3×4 + ... + n(n+1) =
Q43.
Sum: 1/1×3 + 1/3×5 + 1/5×7 + ... to n terms =
Q44.
In a GP, if a₁ + a₂ + a₃ = 13 and a₁a₂a₃ = 27, find the common ratio.
Q45.
Telescoping sum: sum from k=1 to n of [1/k - 1/(k+1)] =
Q46.
The sum of an arithmetic-geometric series a + (a+d)r + (a+2d)r² + ... to infinity (|r|<1) is:
Q47.
If AM of two positive numbers is 5 and HM is 4, their GM is:
Q48.
If x, y, z are in GP and a<sup>x</sup> = b<sup>y</sup> = c<sup>z</sup>, then a, b, c are in:
Q49.
Sum: 1² + 3² + 5² + ... + (2n-1)² =
Q50.
The coefficient of x<sup>n</sup> in the expansion of 1/(1-x)² is:
Q51.
Between two numbers a and b, n geometric means are inserted. The product of all n means equals:
Q52.
If the sum of first n terms is 3n² + 5n, is it AP? Find the common difference.
Q53.
Sum: 1/(1×2×3) + 1/(2×3×4) + ... to n terms =
Q54.
The sum 2 + 2² + 2³ + ... + 2<sup>n</sup> =
Q55.
If three numbers are in HP, their reciprocals are in AP. If HP is 1/2, 1/3, 1/4, the AP is:
Q56.
The number of terms in expansion of (1+x)<sup>n</sup> with r-th term having coefficient nCr is:
Q57.
Sum of the series: 1 + 2x + 3x² + 4x³ + ... to infinity (|x| < 1) =
Q58.
If a, b, c are in GP and p, q, r are in AP, then a<sup>p</sup> × b<sup>q</sup> × c<sup>r</sup> =
Q60.
The sum of the first n odd natural numbers (1 + 3 + 5 + …) is:
Q61.
The sum 1/(1·2) + 1/(2·3) + ... + 1/(10·11) equals:
Q62.
The sum to infinity of 1 + 2/3 + 3/9 + 4/27 + ... (nth term n/3<sup>n−1</sup>) is:
Q63.
The value of 1·2 + 2·2² + 3·2³ + ... + 5·2⁵ (that is Σ n·2ⁿ for n = 1 to 5) is:
Q64.
If the sum of n terms of a series is Sₙ = 3n² + 2n, its 10th term is:
Q65.
The value of 1² − 2² + 3² − 4² + ... + (2n−1)² − (2n)² is:
Q66.
For positive reals a, b, c the minimum value of (a + b + c)(1/a + 1/b + 1/c) is:
Q67.
An infinite GP has sum 15 and the sum of the squares of its terms is 45. Its first term is:
Q68.
The sum of the first n terms of the series 9 + 99 + 999 + ... is:
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