SSC CGL 2025 Tier-I · 16 September 2025, Shift 3 · General Intelligence and Reasoning · Question 13 of 75

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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The 6th term of a geometric progression (GP) is 48. The first term is 1.5. What is the common ratio (CR)?

(a)2.0
(b)3.0
(c)2.5
(d)2.2

Answer

Why

Correct — A.
Rule: the nth term of a GP is a × rⁿ⁻¹, so the 6th term is a × r⁵.

1.5 × r⁵ = 48
r⁵ = 48 ÷ 1.5 = 32
r = 2, since 2⁵ = 32

Check: 1.5, 3, 6, 12, 24, 48 is the 6th term.
Common ratio 2.0 → option (a).

Why the others are wrong

(b)
3.0 — 3⁵ = 243, so a ratio of 3 makes the 6th term 1.5 × 243 = 364.5, far above 48.
(c)
2.5 — 2.5⁵ ≈ 97.66, so a ratio of 2.5 makes the 6th term about 146.5, not 48.
(d)
2.2 — 2.2⁵ ≈ 51.54, so a ratio of 2.2 makes the 6th term about 77.3. The ratio must satisfy r⁵ = 32 exactly.

Concept

In a geometric progression each term is the one before multiplied by the common ratio r. The terms run a, ar, ar², ar³ …, so the nth term is a × rⁿ⁻¹: the power is one less than the term number.

Divide the given term by the first term to isolate the power of r, then find the number that, raised to that power, gives the quotient.

Set in General Intelligence and Reasoning, this is plain algebra. If the fifth root of 32 does not come to mind, build the series from 1.5 with each option until one reaches 48 at the 6th term.

Key facts

The nth term of a GP is a × rⁿ⁻¹.
Powers of 2: 2⁵ = 32 and 2⁶ = 64.
With a = 1.5 and r = 2 the series runs 1.5, 3, 6, 12, 24, 48.

Study next

Sum of the first n terms of a GP: a(rⁿ − 1) ÷ (r − 1)Finding a missing middle term of a GP

Common traps

Using r⁶ for the 6th term: 1.5 × 2⁶ = 96, not 48
Treating the series as arithmetic: 1.5 + 5d = 48 gives d = 9.3, a difference, not a ratio

A GP term is asked the reverse way at 15 Sep 2025, 09:00, Reasoning Q.11: from first term 3.6 and ratio 1.5 it wants the 3rd term, 3.6 × 1.5² = 8.1.

Related PYQs

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Topic: Number Series — all 178 SSC CGL questions on it, every solved shift.