WAEC 2022 · Paper 2 · Q1

Sequences & series (AP, GP)

The third term of an Arithmetic Progression (A.P.) is 23 and the sum of the first seven terms is 210. Find the:

(a)
common difference;
(b)
first term;
(c)
sum of the first 20 terms.

Worked solution (try it first)

Write each fact as an equation.
The third term: $T_3 = a + 2d = 23$ .
The sum of the first seven terms: $S_7 = \frac72[2a + 6d] = 7(a + 3d) = 210$ , so $a + 3d = 30$ .

(a)

Take the first equation from the second: $(a + 3d) - (a + 2d) = 30 - 23$ , so the common difference is $d = 7$ .

(b)

Put $d = 7$ into $a + 2d = 23$ : $a = 23 - 14 = 9$ .

(c)

$S_{20} = \frac{20}{2}[2a + 19d]$
$= 10 \times (18 + 133)$
$= 10 \times 151$
$= 1510$ .

Report a problem with this question