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Question
If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is
Options
4n − 3
3n − 4
4n + 3
3n + 4
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Solution
Here, the sum of first n terms is given by the expression,
Sn = 2n2 + 5n
We need to find the nth term.
So we know that the nthterm of an A.P. is given by,
an = Sn - Sn-1
So,
`a_n = (2n^2 + 5n) - [2(n-1)^2 + 5 (n-1)]`
Using the property,
( a - b)2 = a2 + b2 - 2ab
We get,
`a_n = (2n^2 + 5n) - [2(n^2 + 1 - 2n) + 5 (n-1)]`
= (2n2 + 5n) +- (2n2 + 2 - 4n + 5n - 5)
= 2n2 + 5n - 2n2 - 2 + 4n - 5n + 5
= 4n + 3
Therefore, an = 4n + 3
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