WAEC 2017 · Paper 2 · Q4

Sequences & series (AP, GP)

(a)
If the sixth term of an Arithmetic Progression (A.P.) is 37 and the sum of the first six terms is 147, find the: (i) first term; (ii) sum of the first fifteen terms.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(i)

The sixth term is the last of the first six terms, so use $S_n = \frac{n}{2}(a + l)$ with $l = 37$ : $S_6 = \frac62(a + 37) = 3(a + 37) = 147$ .
So $a + 37 = 49$ , and the first term is $a = 12$ .

(ii)

Find $d$ from the sixth term: $T_6 = a + 5d = 37$ , so $12 + 5d = 37$ , $5d = 25$ and $d = 5$ .
$S_{15} = \frac{15}{2}[2a + 14d]$
$= \frac{15}{2}[24 + 70]$
$= \frac{15}{2} \times 94$
$= 705$ .

Report a problem with this question