Question

The mean of $10$ numbers $7\times 8,10\times 10,13\times 12,16\times 14,\dots$ is ___

Answer 1

Answer: 398

$7\times 8,10\times 10,13\times 12,16\times 14\dots \dots$
$T_n=(3n+4)(2n+6)=2(3n+4)(n+3)$
$=2\left(3n^2+13n+12\right)=6n^2+26n+24$
$S_{10}=\sum _{n=1}^{10}{T}_n=6\sum _{n=1}^{10}{n}^2+26\sum _{n=1}^{10}n+24\sum _{n=1}^{10}1$
$=\frac{6(10\times 11\times 21)}{6}+26\times \frac{10\times 11}{2}+24\times 10$
$=10\times 11(21+13)+240$
$=3980$
Mean $=\frac{S_{10}}{10}=\frac{3980}{10}=398$