Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.


Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.


Here, we are given an A.P. whose $n^{\text {th }}$ term is given by the following expression, $a_{n}=2-3 n$. We need to find the sum of first 25 terms.

So, here we can find the sum of the $n$ terms of the given A.P., using the formula, $S_{n}=\left(\frac{n}{2}\right)(a+l)$

Where, a = the first term

l = the last term

So, for the given A.P,

The first term (a) will be calculated using in the given equation for nth term of A.P.





Now, the last term (l) or the nth term is given

$l=a_{n}=2-3 n$

So, on substituting the values in the formula for the sum of n terms of an A.P., we get,







Therefore, the sum of the 25 terms of the given A.P. is $S_{25}=-925$.

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