If Sn denotes the sum of first n terms of an AP then prove that S12= 3

1.	If Sn denotes the sum of first n terms of an AP then prove that S12= 3 (S8 - S4)
Answer» L.H.S ; S12= 12/2{2a + (12-1)d} = 6{2a + 11*d} = 12a + 66dR.H.S ; 3(S8 - S4) =3[n/2{2a+(n-1)d} - n/2{ 2a+(n-1)d}] = 3{8/2(2a+7d) - 4/2{2a+3d)} =3{4(2a+7d) - 2(2a+3d)} =3(8a+28d - 4a-6d) =3(4a+22d) =12a+66d Therefore ; L.H.S = R.H.S Proved......?????????????????????????????????????????????????

Discussion