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?

If there are (2n + 1) terms in an arithmetic series, then prove that the ratio of the sum of odd terms to the sum of even terms is (n + 1) : n.

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)

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

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