Question

Which term of g.p. (i) 1, 1/3, 1/9, ... is 1/243?

Answer 1

given g.p


1 ,1/3 and 1/9.......1/243
we have to find 1/243 is which term of g.p for that
we have to calculate common ratio
that is r= a2/a1
r=1÷1/3 we get 1/3 as common ratio
nth term of g.p formula
$ar = a . {r}^{n - 1}$
1/243=1.(1/3)^n-1. 1/243 can be written as (1/3)^5=1/3^n-1
then
when bases are equal powers are also equal
then 5=n-1
n= 6
hence 1/243 is the sixth term of g.p