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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