WAEC 2013 · Paper 2 · Q4

(a)

1. The odd numbers $51, 53, \ldots, 99$ form an AP with first term $a = 51$, common difference $d = 2$ and last term $l = 99$.
2. Find the number of terms from $l = a + (n - 1)d$: $99 = 51 + 2(n - 1)$.
3. So $2(n - 1) = 48$, which gives $n - 1 = 24$ and $n = 25$.
4. Use $S_n = \frac{n}{2}(a + l)$: $S_{25} = \frac{25}{2}(51 + 99)$.
5. Work it out: $\frac{25}{2} \times 150 = 1875$.
6. The sum of the odd numbers from 51 to 99 is 1875.