Question

In a geometric sequence , the common ratio and the second term are 2 and 30 respectively. find the value of a and the sum of the first eight terms ?

Answer 1

`a=15 , S_8 =3825`

Explanation:

In geometric sequence `2` nd term is `30 :. a*r=30` and common

ratio is `r=2` , where `a` is the first term , `:. a= 30/2=15`

We know sum of `n` terms in a geometric sequence is

`S_n= (a (r^n-1))/(r-1) :. S_8 = 15*(2^8-1)/(2-1)`

`:. S_8 = 15*(256-1)=15*255=3825`

`:. a=15 , S_8 =3825` [Ans]