If the sum of n terms of an A.P. is 3n^{2} + | vedclass

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(C) Let $a$ be the first term and $d$ be the common difference of the $A.P.$Given the sum of $n$ terms $S_{n} = 3n^{2} + 5n$.The $n^{	ext{th}}$ term

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(C) Let $a$ be the first term and $d$ be the common difference of the $A.P.$Given the sum of $n$ terms $S_{n} = 3n^{2} + 5n$.The $n^{	ext{th}}$ term $a_{n}$ is given by $S_{n} - S_{n-1}$.$a_{n} = (3n^{2} + 5n) - [3(n-1)^{2} + 5(n-1)]$$a_{n} = 3n^{2} + 5n - [3(n^{2} - 2n + 1) + 5n - 5]$$a_{n} = 3n^{2} + 5n - [3n^{2} - 6n + 3 + 5n - 5]$$a_{n} = 3n^{2} + 5n - 3n^{2} + n + 2 = 6n + 2$.Given the $m^{	ext{th}}$ term $a_{m} = 164$.$6m + 2 = 164$$6m = 162$$m = \frac{162}{6} = 27$.Thus,the value of $m$ is $27$.

If the sum of $n$ terms of an $A.P.$ is $3n^{2} + 5n$ and its $m^{\text{th}}$ term is $164$,find the value of $m$.

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