The sum of 3+5+7+ldots to n terms is: | vedclass

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Question

(A) The given series is $3+5+7+\ldots$ up to $n$ terms. This is an Arithmetic Progression $(A.P.)$ with the first term $a = 3$ and common difference $

Vedclass · Accepted Answer

$n(n+2)$

Vedclass · Answer

(A) The given series is $3+5+7+\ldots$ up to $n$ terms. This is an Arithmetic Progression $(A.P.)$ with the first term $a = 3$ and common difference $d = 5 - 3 = 2$. The sum of the first $n$ terms of an $A.P.$ is given by the formula: $S_n = \frac{n}{2}[2a + (n-1)d]$ Substituting the values $a = 3$ and $d = 2$: $S_n = \frac{n}{2}[2(3) + (n-1)2]$ $S_n = \frac{n}{2}[6 + 2n - 2]$ $S_n = \frac{n}{2}[2n + 4]$ $S_n = n(n + 2)$

The sum of $3+5+7+\ldots$ to $n$ terms is:

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