Question

How many terms of the series 2 + 6 + 18 + ............ must be taken to make the sum equal to 728?

Answer 1

Given series: 2 + 6 + 18 + ............

Now, `6/2 = 3, 18/6 = 3`

Thus, given series is a G.P. with first term, a = 2 and common ratio, r = 3  ...(∵ r > 1)

Let the number of terms to be added = n

Then, S_n = 728 

`=> (a(r^n - 1))/(r - 1) = 728`

`=> (2(3^n - 1))/(3 - 1) = 728`

`=>` 3ⁿ – 1 = 728

`=>` 3ⁿ = 729

`=>` 3ⁿ = 3⁶

`=>` n = 6

Hence, required number of terms = 6