JAMB 2015 · UTME · Q13

Which formula represents the general term of the numbers $\left\{-1, \frac23, -\frac12, \frac25, \ldots\right\}$ for $n = 1, 2, 3, 4, \ldots$ ?

Worked solution (try it first)

Write $-1$ as $-\frac22$ and $-\frac12$ as $-\frac24$ .
Then the sizes are $\frac22, \frac23, \frac24, \frac25$ , which is $\frac{2}{n + 1}$ .
The signs go $-, +, -, +$ : negative when $n$ is odd.
That is the pattern of $(-1)^n$ .
So the general term is $(-1)^n\dfrac{2}{n + 1}$ , option C.