WAEC 2018 · Paper 2 · Q4

Sequences, series & binomial expansion

(a)
The sum of the first twelve terms of an Arithmetic Progression is 168. If the third term is 7, find the values of the common difference and the first term.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

The sum: $S_{12} = \dfrac{12}{2}[2a + 11d] = 168$ .
Divide by 6: $2a + 11d = 28$ .
The third term: $a + 2d = 7$ , so $a = 7 - 2d$ .
Substitute: $2(7 - 2d) + 11d = 28$ , so $14 + 7d = 28$ .
So $d = 2$ , and $a = 7 - 4 = 3$ .

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