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S3=3(S2-S1)

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S3=3(S2-S1)

Posted by Himanshi Thakkar 6 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 1 month ago

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

Answer:

Let ‘a’ be the first term of the AP and ‘d’ be the common difference

S₁ = (n/2)[2a + (n – 1)d] --- (1)

S₂ = (2n/2)[2a + (2n – 1)d] = n[2a + (n – 1)d] --- (2)

S₃ = (3n/2)[2a + (3n – 1)d] --- (3)

Consider the RHS: 3(S₂ – S₁)

= S₃

= L.H.S

∴ S₃ = 3(S₂ - S₁) .

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