maths

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For an A.P.
sum of 2n terms = 3* sum of n terms
then
sum of 3n terms : sum of n terms = ?

  • maths -

    given: sum of 2n terms = 3* sum of n terms

    (2n)/2 [2a + (2n-1)d ] = 3(n/2) [2a + (n-1)d ]

    2(2a + 2nd - d) = 3( 2a + nd - d)
    4a + 4nd - 2d = 6a + 3nd - 3d
    -2a = -nd -d
    2a = nd + d

    then
    sum of 3n terms : sum of n terms
    = sum of 3n terms / sum of n terms
    = [ (3n/2) [2a + (3n-1)d ] ] / [ (n/2) [2a + (n-1)d) ]]
    = 3( nd+d + 3nd-d) / (nd+d + nd-d)
    = 3(4nd) / (2nd)
    =12nd/(2nd)
    = 6/1

    or 6 : 1

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