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Question

If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is (a+c)(b+c2a)2(ba).

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Solution

Sn=n2[2a+(n1)d]

b=a+d, ba=d

c=a+(n1)d

c=a+ndd

ca=(n1)(ba)

(n1)=caba,n=caba+1=ca+baba=c+b2aba

d=(ba)

Sn=c+b2a2(ba)[2a+caba(ba)]

Sn=b+c2a2(ba)(a+c)

Sn=(a+c)(b+c2a)2(ba).

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