find the sum of the following arithmetic series 7+13+19+25+…+85

Question

find the sum of the following arithmetic series 7+13+19+25+…+85

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Ayla 2 weeks 2021-09-12T14:22:16+00:00 1 Answer 0

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    2021-09-12T14:23:56+00:00

    Step-by-step explanation:

    Given Arithmetic series is:

    7+13+19+25+…+ 85

    Here,

    First term a = 7

    Common Difference d = 13 – 7 = 6

    last term  t_n= 85

    First let us find the number of terms in given series.

     t_n= a + (n-1)d\\\therefore 85 = 7+ (n-1)\times 6\\\therefore 85 = 7+ 6n-6\\\therefore 85 = 1+ 6n\\\therefore 6n = 85 - 1\therefore 6n = 84\therefore n = \frac{84}{6}\\\therefore n = 14\\

    Hence, given series has total 14 terms.

    Sum of n terms of an Arithmetic series is given as:

    S_n =  \frac{n}{2} (a + t_n) \\  \\  \therefore \: S_{14}=  \frac{14}{2}  \times \: (7 + 85) \\  \\ \therefore \: S_{14}= 7  \times \: 92 \\  \\  \huge \red{ \boxed{\therefore \: S_{14}= 644 }}\\

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