Question

If Sn denotes the sum of first n terms of an AP, prove that S₁₂ = 3(S₈-S₄).

Answer 1

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Let the First term of the A.P be a and Common Difference be d.

=> sum of first n terms :-

Sn  = n/2 {2a+(n-1) d}

Now,

Finding S12 , s8 and s4 seperately. we get,


S₁₂ = 12/2 {2a+(12-1) d}
    =12a+66d


S₈ = 8/2  {2a+7d} 
      = 8a+28d


S₄ = 4/2 {2a+3d}
     = 4a+6d

Now, Taking R.H.S.



3(S₈-S₄) = ?

=> 3[ ( 8a + 28d) - (4a + 6d)]

=> 3 ( 2a + 22d)

=> 6a + 66d = L.H.S.
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