ECZ 2023 · GCE Paper 2 · Question 2 — Sequences and Series

Question from ECZ 2023 · GCE Paper 2 · Question 2

(a) In a geometric progression, the second term is 21 and the fourth term is 189. Calculate the

(a(i)) first term and the common ratio,[3]

Verified working — step 1

In a GP, divide the two given terms to isolate r:

(a(ii)) sixth term,[2]

Verified working — step 1

T_n = a r^n-1, with a = 7 and r = 3.

(a(iii)) sum of the first 5 terms of the progression.[2]

Verified working — step 1

S_n = arⁿ - 1r - 1 with a = 7, r = 3:

(b) Given that matrix P = 7x-2-x1,

(b(i)) find the value of x for which the determinant of P is -10,[2]

Verified working — step 1

det P = (7x)(1) - (-2)(-x) = 7x - 2x = 5x

(b(ii)) hence, find the inverse of P.[2]

Verified working — step 1

With x = -2: P = -14-221 and det P = -10.

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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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