The sum of first 7 term of an a.p. is 49 and that of first 17 term of it is 289. Find the sum of first n term

Question

The sum of first 7 term of an a.p. is 49 and that of first 17 term of it is 289. Find the sum of first n term

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Amelia 30 mins 2021-10-13T12:48:14+00:00 2 Answers 0 views 0

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    0
    2021-10-13T12:49:53+00:00

    Refers to attachment ⚘⚘

    0
    2021-10-13T12:49:56+00:00

    ANSWER:

    S_n =  n^2

    GIVEN:

    S_7 =  49\\S_{17}=289

    FORMULA:

    S_n = n/2(2a + (n-1)d)

    EXPLANATION:

    S_7 = 7/2(2a + (7-1)d)  \\  \\  7(2a + 6d) = 98 \\  \\ 2a = 14 - 6d \\  \\ S_{17} = 17/2(2a + (17 - 1)d)  \\ \\2a + 16d = 17(2) \\ \\  2a = 34 - 16d \\  \\ Equate \: the \: 2a \\  \\ 14 - 6d  =  34 - 16d \\  \\ 10d = 20 \\  \\ d = 2 \\  \\ Substitute \: d = 2 \: in \: 2a = 14 - 6d \\  \\ 2a = 14 - 12 \\  \\ 2a =   2 \\  \\ S_n =  n/2(2 + (n - 1)2) \\  \\ S_n =  n/2(2+(n-1)2)\\  \\ S_n =  n(1+n-1)\\ \\S_n = n^2

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