WAEC 2019 · Paper 2 · Q11

(a)
The third and sixth terms of a Geometric Progression (G.P.) are $\frac14$ and $\frac{1}{32}$ respectively. Find the: (i) first term and the common ratio; (ii) seventh term.
Separate values with commas, e.g. 3, −2
(b)
Given that 2 and $-3$ are the roots of the equation $ax^2 + bx + c = 0$ , find the values of $a$ , $b$ and $c$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

The $n$ th term of a G.P. is $ar^{n - 1}$ .
So $T_3 = ar^2 = \frac14$ and $T_6 = ar^5 = \frac{1}{32}$ .
Divide the sixth term by the third, so that $a$ cancels: $\frac{ar^5}{ar^2} = r^3$
$= \frac{1}{32} \div \frac14$
$= \frac{4}{32}$
$= \frac18$ .
So $r = \frac12$ .
Put $r = \frac12$ into $ar^2 = \frac14$ : $a \times \frac14 = \frac14$ , so $a = 1$ .
The first term is 1 and the common ratio is $\frac12$ .