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Question
If the sum of first n terms is (3n2 + 5n), find its common difference.
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Solution
Let Sn denotes the sum of first n terms of the AP.
∴ sn = 3n2 + 5n
⇒ `s_(n-1) = 3 (n-1) ^2 + 5 (n-1)`
= `3(n^2 - 2n + 1) + 5 (n-1)`
=`3n^2 -n-2`
Now ,
nth term of AP , an = sn - sn-1
= (3n2 + 5n ) - ( 3n2 -n-2)
= 6n + 2
Let d be the common difference of the AP.
∴ d = an - a n-1
= (6n + 2 ) - [ 6(n-1 ) +2]
= 6n + 2 - 6 (n-1) -2
= 6
Hence, the common difference of the AP is 6.
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