Question

Find the 9th term and the general term of the progression: $\frac{1}{4},-\frac{1}{2},1,-2,.......$

Answer 1

The given progression is clearly a G.P with a=1/4 and common ratio r=-2

$\therefore$ the 9th term will be,

$a_9=a{r}^{(9-1)}=a{r}^8=\frac{1}{4}{(-2)}^8=64$

and the general term will be,

$a_n=a{r}^{(n-1)}=\frac{1}{4}{(-2)}^{n-1}={(-1)}^{n-1}\times 2^{n-3}$