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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