ECZ 2018 · O-Level Paper 2 · Question 5 — Sequences and Series
Question from ECZ 2018 · O-Level Paper 2 · Question 5
(a) Simplify b - aa2 - b2.[2]
Verified working — step 1
Factor the denominator: a2 - b2 = (a - b)(a + b).(b) The first three terms of a geometric progression are k + 4, k and 2k - 15 where k is a positive constant.
(b(i)) Find k.[3]
Verified working — step 1
In a GP the ratio between consecutive terms is equal: kk + 4 = 2k - 15k.(b(ii)) List the first three terms of the progression.[2]
Verified working — step 1
Substitute k = 12 into the three expressions.(b(iii)) Calculate the sum to infinity.[2]
Verified working — step 1
Common ratio r = 1216 = 34, and |r| < 1.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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