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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. - Mathematics

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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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Solution

Let the common difference, first term and last term of the AP be d, a and l, respectively.
Suppose the number of terms in the given AP be n.

Sum of n terms of an AP, Sn=n/2 (a+l)


Given:
a = 7
l = 49

Sn=420

`therefore n/2(7+49)=420`

`=>28n=420`

`=>n=420/28=15`

Now an=a+(n-1)d=l

⇒49=7+(15−1)d

⇒49=7+14d

⇒14d=42

⇒d=3

Thus, the common difference of the A.P. is 3.

Concept: Sum of First n Terms of an AP
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