Question

how many terms of the series given above must be taken to amount to 55/72​

Answer 1

Answer:

Let's assume, we take ’n' terms

Sn = {a(1-r^)} / (1-r) , where, Sn denotes the sum of n terms, ‘a’ is the first term.of GP, & r is common ratio. Here, a= 2/9, r = -1/3 ÷ 2/9 = -3/2

=> 55/72 = {2/9 (1- (-3/2)^n ) } / { 1 - (-3/2) }

=> 55/72 = {2/9 ( 1 + (3/2)^n) / 5/2

=>( 55 * 5 * 9)/(72 * 2 *2) = (1+(3/2)^n )

=> (275/32) - 1 = (3/2)^n

=> 243/32 = (3/2)^n

=> (3/2)^5 = (3/2)^n

=> n = 5

5 terms to be taken