IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 22

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Sequences and Series, with the answer and a step-by-step solution.

Sequences and SeriesAlgebraMultiple choiceMedium
The first three terms of an increasing geometric progression are positive. Their sum is 26, and their product is 216. What is the fourth term?
  1. A
    54
  2. B
    72
  3. C
    36
  4. D
    162
Pick an option, then check.
Answer & solution

Answer: Option A

Write the three terms symmetrically as a/r, a and ar.

Their product is a³ = 216, so a = 6.

Their sum is 6/r + 6 + 6r = 26, so 6/r + 6r = 20.

Multiplying through by r: 6 + 6r² = 20r, that is 3r² − 10r + 3 = 0.

Factorising: (3r − 1)(r − 3) = 0, so r = 3 or r = 1/3.

The progression is increasing, so r = 3 and the terms are 2, 6, 18.

The fourth term = 18 × 3 = 54.

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