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Question
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.
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