Find the sum of the first 20 terms of the geometric series .

The ratio of the sums of first m and first n terms of an arithmetic series is m²: n²show that the ratio of the mth and nth terms is (2m – 1) : (2n – 1)

A gardener plans to construct a trapezoidal shaped structure in his garden. The longer side of trapezoid needs to start with a row of 97 bricks. Each row must be decreased by 2 bricks on each end and the construction should stop at 25th row. How many bricks does he need to buy?

Find the sum of the first 27 terms of the geometric series .

Find S_nfor each of the geometric series described below.

(i) a = 3, t₈ = 384, n = 8. (ii) a = 5, r = 3, n = 12.

Ans. 765