Question

The common ratio of a finite GP is 3, and its last term is 486. If the sum of these terms is 728, find the first term.

Answer 1

‘T_n’ represents the nth term of a G.P. series. 

T_n = ar^n-1 

⇒ 486 = a(3)^n-1 

⇒ 486 = a( 3n ÷ 3)) 

⇒ 486 × 3 = a(3ⁿ) 

⇒ 1458 = a(3ⁿ) ………(i)

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

‘S_n’ represents the sum of the G.P. series up to n^th terms, 

‘a’ represents the first term, 

‘r’ represents the common ratio and 

‘n’ represents the number of terms.