Find S15 of the series : 2 + 5 + 10 + 17 + 26 + -.​

Question

Find S15 of the series : 2 + 5 + 10 + 17 + 26 + …..​

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Sadie 1 month 2021-10-27T02:44:36+00:00 1 Answer 0 views 0

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    2021-10-27T02:46:32+00:00

    Step-by-step explanation:

    Given:2 + 5 + 10 + 17 + 26 + …..

    To find:S15

    Solution:

    To find the sum of first 15 terms of given series,first check the pattern of series

    2 + 5 + 10 + 17 + 26 + ... \\  \\ ( {1)}^{2}  + 1 + ( {2)}^{2}  + 1 + ( {3)}^{2}  + 1 + ( {4})^{2}  + 1  + ( {5)}^{2}  + 1 + ... \\  \\

    So,

    general term of this series is

    T_n =  {n}^{2}  + 1 \\  \\

    To find the sum of n terms of the series

    S_n =  \Sigma(T_n) \\  \\ S_n =  \Sigma( {n}^{2}  + 1) \\  \\

    Sum of 15 terms

    S_{n} = _{n = 1} ^{15}  \Sigma( {n}^{2}  + 1) \\  \\ S_n =_{n = 1} ^{15}  \Sigma {n}^{2}  +  _{n = 1} ^{15}\Sigma \: 1 \\ \\   S_{n}=  \frac{n(n + 1)(2n + 1)}{6}  + n \\  \\  S_{15}=  \frac{15(15 + 1)(15 \times 2 + 1)}{6}  + 15 \\  \\  S_{15}=  \frac{15 \times 16 \times 31}{6}  + 15 \\  \\  S_{15}= 5 \times 8 \times 31 + 15 \\  \\ S_{15}= 40 \times 31 + 15 \\  \\ S_{15}= 1240 + 15 \\  \\ S_{15} = 1255 \\  \\

    Sum of 15 terms of the series is 1255.

    Hope it helps you.

    To learn more on brainly:

    1)find the nth term of the 2,4,9,16,25

    https://brainly.in/question/7706998

    2)find the sum of the following series 1+4+9+16+…+225

    https://brainly.in/question/9797431

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