Question

The $n$th term of an A.P is given by $T_n=10-6n$. Find the sum of first $n$ terms of the A.P

Answer 1

$T_r=10-6r$

summation of first n term = $\sum _{x=1}^{n}Tr$

$=\sum _{r-1}^{n}10-6r$

$=10n-6\frac{n(n+1)}{2}$

$=10n-3n(n+1)=n(10-3n-3)$

$=n(7-3n)$

$=7n-3n^2$