WAEC 2010 · Paper 2 · Q2

Sequences, series & binomial expansion

(a)
If the sum of the first $n$ terms of the series $4 + 7 + 10 + \dots$ is $209$ , find $n$ .

Worked solution (try it first)

The series is an A.P. with $a = 4$ and $d = 3$ .
Use $S_n = \dfrac n2[2a + (n - 1)d]$ : $\dfrac n2[8 + 3(n - 1)] = 209$ .
Simplify the bracket: $\dfrac n2(3n + 5) = 209$ .
Multiply by 2 and rearrange: $3n^2 + 5n - 418 = 0$ .
Factorise: $(3n + 38)(n - 11) = 0$ .
$n$ must be a positive whole number, so $n = 11$ .

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