ECZ 2026 · GCE Paper 2 · Question 3 — Sequences and Series
Question from ECZ 2026 · GCE Paper 2 · Question 3
(a) The second and fourth terms of a geometric progression are 6 and 1.5 respectively. Find the
(a(i)) common ratio and the first term,[3]
Verified working — step 1
Tn = a rn-1, so T2 = ar = 6 and T4 = ar3 = 1.5.(a(ii)) 8th term,[2]
Verified working — step 1
T8 = a r7(a(iii)) sum to infinity of the progression.[2]
Verified working — step 1
|r| = 0.5 < 1, so the sum to infinity exists: S = a1 - r.(b) Evaluate ∫1-1 (3 - 4x + 9x2 - 4x3) dx.[3]
Verified working — step 1
Integrate term by term: the antiderivative is 3x - 2x2 + 3x3 - x4.The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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