The mean of 10 numbers 7 times 8, 10 times 10 | vedclass

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(D) The given sequence is $T_n = (3n+4)(2n+6)$ for $n = 1, 2, \ldots, 10$.Expanding the expression: $T_n = 6n^2 + 18n + 8n + 24 = 6n^2 + 26n + 24$.The

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$398$

Vedclass · Answer

(D) The given sequence is $T_n = (3n+4)(2n+6)$ for $n = 1, 2, \ldots, 10$.Expanding the expression: $T_n = 6n^2 + 18n + 8n + 24 = 6n^2 + 26n + 24$.The sum of the first $10$ terms is $S_{10} = \sum_{n=1}^{10} (6n^2 + 26n + 24)$.Using summation formulas:$S_{10} = 6 \sum_{n=1}^{10} n^2 + 26 \sum_{n=1}^{10} n + \sum_{n=1}^{10} 24$.$S_{10} = 6 \left( \frac{10(11)(21)}{6} \right) + 26 \left( \frac{10(11)}{2} \right) + 24(10)$.$S_{10} = 2310 + 1430 + 240 = 3980$.The mean is $\frac{S_{10}}{10} = \frac{3980}{10} = 398$.

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

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