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Sum of the first 15 terms of the series 2 2 +5 2 +8 2 +....... is options are 10415 10425 10440 10455

  1. Sum of the first 15 terms of the series 22+52+82+....... is 
options are
10415
10425
10440
10455

Grade:12th pass

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
7 years ago
Hi,

Please find the solution

22+52+82+......15 terms
=22+52+82+.....+442
=\sum_{n=0}^{14} (2 + 3n)^2
=\sum_{n=0}^{14} (4 + 9n^2 + 12n)
=\sum_{n=0}^{14} 4 + 9\sum_{n=0}^{14}n^2 + 12\sum_{n=0}^{14}n
=4\times 15 + 9 \frac{14(14+1)(2*14+1)}{6} + 12 \frac{14*(14+1)}{2}
Now solve this



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