Question

if sn denotes the sum of 1st n terms of ap.prove that s12=3(s8-s4)

Answer 1

s8 = 4( 2a + 7d)
s4 = 2(2a+ 3d)
s8 - s4 = 4a +22d
3( s8-s4) = 12a + 66d

s12 = 6( 2a + 11d)
= 12a + 66d

Answer 2

Answer:

Step-by-step explanation:

LHS = S12

S12 = N(N+1)/2

S12 = 12(12+1)/2

S12 = 6(13)

S12 =78

RHS = 3(S8-S4)

=3(8(8+1)-4(4+1))/2

=3(72-20)/2

=3(52)/2

=3(26)/2

=78

LHS=RHS

HENCE PROVED