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If the sum of first 7 …

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If the sum of first 7 terms of an AP is 49 and that of 17th term is 289. Find the Sum of first n terms?

    • Posted by Sandeep Sahu 6 years, 3 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 6 years, 3 months ago

    Given that,

    S7 = 49
    S17 = 289
    S7

     = 7/2 [2a + (n - 1)d]
    S7 = 7/2 [2a + (7 - 1)d]
    49 = 7/2 [2a + 16d]
    7 = (a + 3d)
    a + 3d = 7 ... (i)
    Similarly,
    S17 = 17/2 [2a + (17 - 1)d]
    289 = 17/2 (2a + 16d)
    17 = (a + 8d)
    a + 8d = 17 ... (ii)
    Subtracting equation (i) from equation (ii),
    5d = 10
    d = 2
    From equation (i),
    a + 3(2) = 7
    a + 6 = 7
    a = 1
    Sn = n/2 [2a + (n - 1)d]
    = n/2 [2(1) + (n - 1) × 2]
    = n/2 (2 + 2n - 2)
    = n/2 (2n)
    = n2 

    2Thank You

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