The sum of all the terms of a finite A.P. hav | vedclass

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Question

(A) For a finite Arithmetic Progression $(A.P.)$ with $n$ terms,let $a$ be the first term and $l$ be the last term (also denoted as $a_{n}$). The sum

Vedclass · Accepted Answer

$\frac{1}{2} n(a+l)$

Vedclass · Answer

(A) For a finite Arithmetic Progression $(A.P.)$ with $n$ terms,let $a$ be the first term and $l$ be the last term (also denoted as $a_{n}$). The sum of $n$ terms of an $A.P.$ is given by the formula: $S_{n} = \frac{n}{2} [2a + (n-1)d]$ Since the last term $l = a + (n-1)d$,we can substitute this into the sum formula: $S_{n} = \frac{n}{2} [a + a + (n-1)d]$ $S_{n} = \frac{n}{2} [a + l]$ Thus,the correct expression is $\frac{1}{2} n(a+l)$.

The sum of all the terms of a finite $A.P.$ having $n$ terms is given by $S_{n} = \ldots \ldots \ldots$

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