arithmetic

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the sum of the n termsof an ap whose first term is 5 and common difference is 36 is equal to the sum of 2n terms of another AP whose first term is 36 ans common difference is 5. Find n?

  • arithmetic -

    sum of n terms of 1st = (n/2)(10 + 36(n-1))
    = (n/2)(36n - 26)
    sum of 2n terms of 2nd = (2n/2)(72 + 5(2n-1))
    = n(10n + 67)

    (n/2)(36n - 26) = n(10n + 67)
    divide by n, and multiply by 2
    36n - 26 = 20n + 134
    16n = 160
    n = 10

    check:
    sum(10 for 1st) = 5(10 + 36(9)) = 1670
    sum(20 for 2nd) = 10(72 + 19(5)) = 1670
    all is good!

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