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  • The Sum of n,2n,3n terms of an AP are S1, S2, S3 respectively .Prove that S3=3(S2-S1)

The Sum of n,2n,3n terms of an AP are S1, S2, S3 respectively .Prove that S3=3(S2-S1)

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Solution: Let a be the first  term  and d be the common diffrence of the given AP

S_1=n/2[2a+(n-1)d] ............(1)\ \Rightarrow S_2=2n/2[2a+( 2n-1)d] ............(2)\ \S_3=3n/2[2a+(3n-1)d] .....(3)

Now,         S_2-S_1=2n/2[2a+(2n-1)d]-n/2[2a+(n-1)d]\ \Rightarrow S_2-S_1=n/2[2a+(3n-1)d]\ \ herefore 3(S_2-S_1)=3n/2[2a+(3n-1)d]\ \Rightarrow 3(S_2-S_1)=S_3

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Deependra Verma

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