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MathematicsTopic Question Bank50+ Solved MCQsUpdated October 2026👁️ 3.8k Topic Views

Sequences and Series Questions & Answers

Master problem-solving techniques, shortcut tricks, and formulas for Sequences and Series. Solve graded practice questions with complete step-by-step mathematical solutions.

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Sequences and Series — Key Concepts & Shortcuts

•Master core formulas and fundamental algebraic/arithmetic principles for Sequences and Series.
•Apply approximation techniques and calculation shortcuts to solve problems within 45 seconds.
•Practice 2-tier questions and review step-by-step derivations for complex problems.

Practice Questions for Sequences and Series

18+ Solved MCQs

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If f(x) = (x − a)(x − b) + (x − b)(x − c) + (x − c)(x − a), and a, b, c are in Arithmetic Progression (AP), then f'(a), f'(b), and f'(c) are in which progression?

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Sequences and Series Questions & Answers

Sequences and Series — Key Concepts & Shortcuts

Practice Questions for Sequences and Series

If f(x) = (x − a)(x − b) + (x − b)(x − c) + (x − c)(x − a), and a, b, c are in Arithmetic Progression (AP), then f'(a), f'(b), and f'(c) are in which progression?

If 1 + (1 - 22 × 1) + (1 - 42 × 3) + (1 - 62 × 5) + ... + (1 - 202 × 19) = α - 220β, then the ordered pair (α, β) is equal to:

Let a1, a2, ..., an be a given A.P. whose common difference is an integer and Sn = a1 + a2 + ... + an. If a1 = 1, an = 300 and 15 ≤ n ≤ 50, then the ordered pair (Sn-4, an-4) is equal to:

If |x| < 1, |y| < 1 and x ≠ y, then the sum to infinity of the series (x + y) + (x2 + xy + y2) + (x3 + x2y + xy2 + y3) + ... is:

The product 214 × 4116 × 8148 × 161128 × ... to ∞ is equal to:

The sum ∑n=17 n(n + 1)(2n + 1)4 is equal to:

If S = 75 + 952 + 1353 + 1954 + &dots;, then 160S is equal to:

The sum ∑k=120 (1 + 2 + 3 + ... + k) is:

Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference d. If the fourth term of the GP is 3r2, then r2 - d is equal to:

Find the sum of the first 10 terms of the series: 312 × 22 + 522 × 32 + 732 × 42 + &dots;

If 0 < x < 1, then the infinite series 32x2 + 53x3 + 74x4 + ... is equal to:

Let a1, a2, ..., a10 be an A.P. with common difference -3 and b1, b2, ..., b10 be a G.P. with common ratio 2. Let ck = ak + bk for k = 1, 2, ..., 10. If c2 = 12 and c3 = 13, then ∑k=110 ck is equal to:

The number of elements in the set {n ∈ {1, 2, 3, ..., 100} | (11)n > (10)n + (9)n} is:

If [x] denotes the greatest integer less than or equal to x, then the value of ∑n=8100 [(-1)n n2] is equal to:

If the value of (1 + 23 + 632 + 1033 + ... upto ∞)log0.25(13 + 132 + 133 + ... upto ∞) is l, then l2 is equal to:

If ∑r=110 r! (r3 + 6r2 + 2r + 5) = α(11!), then the value of α is equal to:

Which one of the following sequences is NOT convergent?

The infinite series 11p + 12p + 13p + ... ∞ is convergent if:

Frequently Asked Questions on Sequences and Series