The nth term of an A.P is given by

Question:

The $n$th term of an A.P is given by $(-4 n+15)$, Find the sum of first 20 terms of this A.P.

Solution:

$a_{n}=-4 n+15$

$\Rightarrow a_{1}=-4+15=11$

Also, $a_{2}=-8+15=7$

Common difference, $d=a_{2}-a_{1}=7-11=-4$

Now,

$S_{20}=\frac{20}{2}[2 \times 11+(20-1)(-4)]$

$=10(22-76)$

$=-540$

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