Question

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

Answer 1

s12=3 (s8-s4)

s12= 12/2 [2a+(12-1)d]

6 [2a+11d] 1

s8=8/2 [2a+(8-1)d]

4[2a+7d] 2

s4=4/2 [2a+(4-1)d]

2 [2a+3d] 3

keep eq.123 on its place

6 (2a+11d)=3 [4 (2a+7d)-2 (2a+3d)]

12a+66d=3 (8a+28d-4a-6d)

=3 (4a+22d)

=12a+66d

hence proved

Answer 2

Answer:

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