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#### Question

The sum of three numbers in A.P. is –3, and their product is 8. Find the numbers

#### Solution

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A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 1/4 m and a tread of 1/2 m (See figure) calculate the total volume of concrete required to build the terrace.

[Hint : Volume of concrete required to build the first step = 1/4 x 1/2 x 50m^{3}]

If the sum of the first *n* terms of an A.P. is `1/2`(3n^{2} +7n), then find its *n*^{th} term. Hence write its 20^{th} term.

How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636?

The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.