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QJEEM21Maac90: JEE Main 2021 Mathematics - Class 11 JEEM21Maac90 Solution: The mean of 10 numbers 7 8, 10 10, 13 12, 16 14, ....... is…

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

Step-by-Step Verified Solution

7 ×\times 8, 10 ×\times 10, 13 ×\times 12, 16 ×\times 14 ........

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

= 2(3n2 + 13n + 12) = 6n2 + 26n + 24

S10 = ∑n=110Tn=6∑n=110n2+26∑n=110n+24∑n=1101\sum\limits_{n = 1}^{10} {{T_n}} = 6\sum\limits_{n = 1}^{10} {{n^2}} + 26\sum\limits_{n = 1}^{10} n + 24\sum\limits_{n = 1}^{10} 1

=6(10×11×21)6+26×10×112+24×10= {{6(10 \times 11 \times 21)} \over 6} + 26 \times {{10 \times 11} \over 2} + 24 \times 10

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

= 3980

Mean =S1010=398010=398= {{{S_{10}}} \over {10}} = {{3980} \over {10}} = 398

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