ECZ 2019 · GCE Paper 2 · Question 1 — Sequences and Series

In a geometric progression, the third term is 16 and the fifth term is 4.

(a) Simplify (10x³ y² / 35x⁵ y⁴) ÷ (2x² y² / 7x⁴ y²).[2]

Verified working — step 1

Dividing by a fraction is the same as multiplying by its reciprocal.

(b(i)) Calculate the first term and the common ratio.[3]

Verified working — step 1

Let first term = a, common ratio = r.

(b(ii)) Calculate the tenth term.[2]

Verified working — step 1

nth term = a r^n-1

(b(iii)) Calculate the sum to infinity.[2]

Verified working — step 1

Since |r| < 1, sum to infinity = 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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