# Solution - Sum of First n Terms of an AP

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ConceptSum of First n Terms of an AP

#### Question

Find the sum of 20 terms of the A.P. 1, 4, 7, 10, ……

#### Solution

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#### Similar questions

If Sn denotes the sum of first n terms of an A.P., prove that S30 = 3[S20S10]

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Show that a1, a… , an , … form an AP where an is defined as below

an = 9 − 5n

Also find the sum of the first 15 terms in each case.

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In an AP

Given a = 8, an = 62, Sn = 210, find n and d.

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If the ratio of the sum of first n terms of two A.P’s is (7n +1): (4n + 27), find the ratio of their mth terms.

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In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.

A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 ×(5 + 3)]

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