​ The first term of a GP is 27, and its 8th term is 1/81. Find the sum of its first 10 terms. ​

Question

The first term of a GP is 27, and its 8th term is \(\frac{1}{81}\) . Find the sum of its first 10 terms.

Answer 1

‘T_n’ represents the n^th term of a G.P. series. 

T_n = ar^n-1

Sum of a G.P. series is represented by the formula, S_n = a\(\frac{1- r^n}{1-r}\), when |r|<1. 

‘Sn’ represents the sum of the G.P. series up to nth terms, 

‘a’ represents the first term, 

‘r’ represents the common ratio and 

‘n’ represents the number of terms. 

Here, 

a = 27 

r = (ratio between the n term and n-1 term)\(\frac{1}{3}\) 

n = 10 terms