ECZ 2025 · GCE Paper 2 · Question 1 — Sequences and Series

Question from ECZ 2025 · GCE Paper 2 · Question 1

(a) Simplify (a² b³ / 2c) × (ac² / 2b) ÷ (b² c2a).[2]

Verified working — step 1

Change division to multiplication by the reciprocal:

(b(i)) For the geometric progression 60, 30, 15, ..., find the 6th term.[2]

Verified working — step 1

First term a = 60, common ratio r = 3060= 12

(b(ii)) Find the geometric mean of 15 and 3.75.[2]

Verified working — step 1

Geometric mean of two numbers x and y = √(xy)

(b(iii)) Find the sum to infinity.[3]

Verified working — step 1

For |r| < 1, sum to infinity: S∞ = a1 - r

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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