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The sum of n,2n, 3n terms of an A.P are S1,S2, S3 . Prove that S3 = 3(S2-S1)

Posted by Mausam Chahal 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Ayesha P 6 years, 10 months ago

S1= sum of n terms = n|2{2a+(n-1)d} S2= sum of 2n terms = 2n|2{2a+(2n-1)d} S3= sum of 3n terms= 3n|2{2a+(3n-1)d} Lhs=3(S2-S3)=2n|2 {2a+(2n-1)d} - n|2 {2a+(n-1)d} =3n|2{2a+(3n-1)d} Hence S3=3(S2-S1)

0Thank You

Gaurav Seth 6 years, 10 months ago

Let the first term of the A.P. be a and the common difference be d.

According the question,

We have to prove that S₃ = 3 ( S₂ – S₁).

R.H.S = 3 (S₂ – S₁)

= S₃

= L.H.S

⇒ S₃ = 3 ( S₂ – S₁)

0Thank You

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