NECO 2024 · Paper 2 · Q2

(a)
The 4th and 7th terms of a geometric progression are 8 and $\frac{64}{27}$ respectively. Find the (i) common ratio; (ii) first term.
Separate values with commas, e.g. 3, −2
(b)
Express $4231_{\text{five}}$ in denary.

Worked solution (try it first)

(a)(i)

In a G.P., $T_n = ar^{n - 1}$ , so $T_4 = ar^3 = 8$ and $T_7 = ar^6 = \frac{64}{27}$ .
Divide: $r^3 = \frac{64/27}{8} = \frac{8}{27}$ , so $r = \frac23$ .

(ii)

$a = \frac{8}{r^3}$
$= 8 \times \frac{27}{8}$
$= 27$ .

(b)

The place values in base five are 125, 25, 5 and 1: $4231_{\text{five}} = 4 \times 125 + 2 \times 25 + 3 \times 5 + 1$
$= 500 + 50 + 15 + 1$
$= 566$ .

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