Question

how many terms of the series 1+3 +3^2+3^3 must be taken to make 3280​

Answer 1

Here we're given a geometric series with first term, a = 1, and common ratio, r = 3.

Let 3280 be the sum of first n terms of the series, i.e.,

a(rⁿ - 1) / (r - 1) = 3280

1 (3ⁿ - 1) / (3 - 1) = 3280

(3ⁿ - 1) / 2 = 3280

3ⁿ - 1 = 6560

3ⁿ = 6561 = 3^8

=> n = 8

Hence first 8 terms should be added to get the sum 3280.