# Solution - Sum of First n Terms of an AP

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ConceptSum of First n Terms of an AP

#### 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 50m3]

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If the sum of the first n terms of an A.P. is 1/2(3n2 +7n), then find its nth term. Hence write its 20th term.

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

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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.

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

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#### Reference Material

Solution for concept: Sum of First n Terms of an AP. For the course 8th-10th CBSE
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