Question

if sn denotes the sum of the first n terms of an ap prove that s12 =3 (s8-s4)​

Answer 1

Answer:

l dont know this answer sorry ...............

Answer 2

Answer:

let a be the first term and d the common difference.

S12 = (12/2) (2a + (12-1)d)

= 6(2a + 11d)

S12 = 12a + 66d.........(1)

S8 = (8/2)(2a + (8-1)d)

= 4(2a + 7d)

S8 =. 8a + 28d...........(2)

S4 = (4/2)(2a + (4-1)d)

= 2(2a + 3d)

S4 = 4a + 6d...............(3)

now, LHS

S12 = 12a + 66d

= 3(4a + 22d)

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

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

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

= 3( S8 - S4)

= RHS proved