The n^{th} term of an A.P. is given by T_{n} | vedclass

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(A) Given the $n^{th}$ term of the $A.P.$ is $T_{n} = 8n + 3$.To find the sum of the first $n$ terms $(S_{n})$,we use the formula $S_{n} = \frac{n}{2}

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$4n^2 + 7n$

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(A) Given the $n^{th}$ term of the $A.P.$ is $T_{n} = 8n + 3$.To find the sum of the first $n$ terms $(S_{n})$,we use the formula $S_{n} = \frac{n}{2} [a + l]$,where $a$ is the first term and $l$ is the $n^{th}$ term.First term $(a)$ = $T_{1} = 8(1) + 3 = 11$.$n^{th}$ term $(l)$ = $T_{n} = 8n + 3$.Substituting these values into the sum formula:$S_{n} = \frac{n}{2} [11 + (8n + 3)]$$S_{n} = \frac{n}{2} [8n + 14]$$S_{n} = n [4n + 7]$$S_{n} = 4n^{2} + 7n$.

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 8n + 3$. Find the sum of the first $n$ terms of the $A.P.$

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