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If Sn' the sum of first n terms of an AP...

If `S_n' the sum of first n terms of an AP is given by `2n^2+n`, then find its nth term

Text Solution

Verified by Experts

The correct Answer is:
23145
We have `S_(n)=2n^(2)+3n`
`thereforea_(n)=S_(n)-S_(n-1)`
`=2n^(2)+3n-2(n-1)^(2)-3(n-1)`
=4n+1
Therefore, the sequence is 5,9,13…
`thereforeunderset(1leiltjle10)(SigmaSigma)a_(i)a_(j)=(sum_(i=1)^(10)sum_(j=1)^(10)(4i+1)cdot(4j+1)-sum_(i=1)^(10)(4i+1)^(2))/2`
`=((sum_(i=1)^(10)(4i+1))^(2)-sum_(i=1)^(10)(4i+1)^(2))/2`
=23145
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