If the sum of n terms of an A.P. is 2n^2 + 5n | vedclass

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(A) Given that the sum of $n$ terms is $S_n = 2n^2 + 5n$.The $n^{th}$ term $T_n$ is given by the formula $T_n = S_n - S_{n-1}$ for $n > 1$.First,calcu

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$4n + 3$

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(A) Given that the sum of $n$ terms is $S_n = 2n^2 + 5n$.The $n^{th}$ term $T_n$ is given by the formula $T_n = S_n - S_{n-1}$ for $n > 1$.First,calculate $S_{n-1}$:$S_{n-1} = 2(n-1)^2 + 5(n-1)$$S_{n-1} = 2(n^2 - 2n + 1) + 5n - 5$$S_{n-1} = 2n^2 - 4n + 2 + 5n - 5$$S_{n-1} = 2n^2 + n - 3$Now,find $T_n$:$T_n = (2n^2 + 5n) - (2n^2 + n - 3)$$T_n = 2n^2 + 5n - 2n^2 - n + 3$$T_n = 4n + 3$Alternatively,for $n=1$,$T_1 = S_1 = 2(1)^2 + 5(1) = 7$. Using the formula $4n+3$,$4(1)+3 = 7$,which matches.

If the sum of $n$ terms of an $A.P.$ is $2n^2 + 5n$,then the $n^{th}$ term will be

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