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[Solved] The mean of 10 numbers 7 × 8, 10 × 10, 13 × 12, 16 × 14, …. is _________.

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The mean of 10 numbers

7 × 8, 10 × 10, 13 × 12, 16 × 14, …. is _________.

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7 × 8, 10 × 10, 13 × 12, 16 × 14 ……

Tn = (3n + 4) (2n + 6) = 2(3n + 4) (n + 3)

= 2(3n2 + 13n + 12) = 6n2 + 26n + 2

S10 = \(\displaystyle\sum_{n=1}^{10}T_n\) = \(6\displaystyle\sum_{n=1}^{10}n^2\) + \(26\displaystyle\sum_{n=1}^{10}n\) + \(24\displaystyle\sum_{n=1}^{10}1\)

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

= 10 x 11 (21 + 13) + 240

= 3980

Mean = \(\frac{S_{10}}{10}\) = \(\frac{3980}{10}\)

= 398

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