Question

If the nth term of a GP `2,8,32,...` is `131072,` then the value of n is

Answer 1

In the given GP, we have `a=2` and `r=8/4=4`.
Let its nth term be 131072. Then,
`T_(n)=131072 rArr ar^((n-1))=131072`
`rArr 2xx4^((n-1))=131072`
`rArr 4^((n-1))=65536=4^(8)`
`rArr n-1=8 rArr n=9`.
Hence, the 9th term of the given GP is 131072.