The sum of some terms of G.P.is 315 . whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

Explanation

Let the sum of `n` terms be 315 and `a=5, r=2`

i.e., `.a(r^n-1)/r-1=315 , 5(2^n-1)/2-1=315 , 2^n=63+1=64 2^n=2^6 rarr n=6`

Last term `=n^ th ` term `=6^ th ` term `=` a. `r^n-1=5 xx 2^6-1=5 xx 2_1^5=5 xx 32=160`

Last term `=160` and the number of terms `=6`