Find the sum of the series $3^2$ + $5^2$ + $7^2$ +-----upto 10 terms

Question

$\begin{array}{1 1} 1660 \\ 679 \\ 1770 \\ 1540 \end{array}$

Answer 1

Answer : (c) 1770

Explanation :

$T_{n}=(2n+1)^2$

$\sum\;T_{n}=(2n+1)^2$

$=\sum\;(4n^2+4n+1)$

$S_{n}=\large\frac{4n(n+1)(2n+1)}{6}+4\large\frac{n(n+1)}{2}+n$

$S_{10}=\large\frac{4*10*11*21}{6}+4*\large\frac{10*11}{2}+10$

$=1540+220+10$

$=1770.$