Question

the sum of first 15 terms of the series 2 square+5 square+8 square

Answer 1

The sum of first 15 =125

Answer 2

Given series, $2^{2}, 5^{2}, 8^{2}, 11^{2},....$

We have to find the sum,

$S_{n}=2^{2}+ 5^{2}+ 8^{2}+ 11^{2},....$ up to 15 terms

$S_{n}=2^{2}+ 5^{2}+ 8^{2}+ 11^{2},....44_{2}$

$\sum_{n=0}^{14}(3n-1)^{2}$

$\sum_{n=0}^{14}(1+9n^{2}-6n)\\\sum_{n=0}^{14}1+\sum_{n=0}^{14}9n^{2}-\sum_{n=0}^{14}6n\\=1\times 15+9\times \frac{15(15+1)(2\times 15+1)}{6}-6\times \frac{15(15+1)}{2}\\=15+11160-720\\=10455$

To learn about finding the sum of series, click on the given links:

https://brainly.in/question/2047925?msp_srt_exp=5

https://brainly.in/question/6214396?msp_srt_exp=5

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