WAEC 2019 · Paper 2 · Q2

Sequences, series & binomial expansion

(a)
The fourth and sixth terms of a Geometric Progression (G.P.) are 54 and 486 respectively. If $r > 0$ , find the third term.

Worked solution (try it first)

The fourth term: $ar^3 = 54$ .
The sixth term: $ar^5 = 486$ .
Divide: $r^2 = \dfrac{486}{54} = 9$ , so $r = 3$ (the ratio is positive).
Then $a = \dfrac{54}{27} = 2$ .
The third term is $ar^2 = 2 \times 9 = 18$ .

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