NECO 2023 · Paper 1 · Q5

Find the sum of the first 9 terms of the exponential sequence $18, 6, 2, \dots$

Worked solution (try it first)

The first term is $a = 18$ and the common ratio is $r = \dfrac{6}{18} = \dfrac13$ .
For $r < 1$ use $S_n = \dfrac{a(1 - r^n)}{1 - r}$ : $S_9 = \dfrac{18\left(1 - \left(\frac13\right)^9\right)}{\frac23}$ .
$18 \div \frac23 = 27$ and $\left(\frac13\right)^9 = \frac{1}{19683}$ , so $S_9 = 27\left(1 - \frac{1}{19683}\right)$
$\approx 26.9986$ .
To two decimal places this is 27.00, option E.