The mean of 10 numbers

Question:

The mean of 10 numbers

$7 \times 8,10 \times 10,13 \times 12,16 \times 14, \ldots .$ is________.

Solution:

$7 \times 8,10 \times 10,13 \times 12,16 \times 14 \ldots \ldots$

$\mathrm{T}_{\mathrm{n}}=(3 \mathrm{n}+4)(2 \mathrm{n}+6)=2(3 \mathrm{n}+4)(\mathrm{n}+3)$

$=2\left(3 n^{2}+13 n+12\right)=6 n^{2}+26 n+24$

$S_{10}=\sum_{n=1}^{10} T_{n}=6 \sum_{n=1}^{10} n^{2}+26 \sum_{n=1}^{10} n+24 \sum_{n=1}^{10} 1$

$=\frac{6(10 \times 11 \times 21)}{6}+26 \times \frac{10 \times 11}{2}+24 \times 10$

$=10 \times 11(21+13)+240$

$=3980$

Mean $=\frac{\mathrm{S}_{10}}{10}=\frac{3980}{10}=398$

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