3hey dude group the similar terms.
(Sn-3Sn+3Sn-Sn)+3-2+1=0+2
which is not possible so the qn is rong.
if Sn be the sum of n consecutive terms of an A.P.show that (Sn+3)-(3Sn+2)+(3Sn+1)-Sn=0
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341He has made a small mistake in a sign.
It is evident that the sequence {Si+1-Si} is an AP.
So, that means Sn+3-Sn+2, Sn+2-Sn+1, Sn+1-Sn are in A.P.
(Sn+3-Sn+2)-(Sn+2-Sn+1) =(Sn+2-Sn+1) - (Sn+1-Sn)
Rearranging the terms gives Sn+3-3Sn+2+3Sn+1-Sn=0
In the theory of finite differences LHS is known as the 3rd order forward difference operator, and that it equals zero tells us that the sequence is characterised by a quadratic, i.e. tn =an2+bn+c
