Solveeit Logo

Question

Question: If S<sub>1</sub>, S<sub>2</sub>, S<sub>3</sub> are the sum of n. 2n, 3n terms of an A.P. then 3(S<su...

If S1, S2, S3 are the sum of n. 2n, 3n terms of an A.P. then 3(S2 –S1) =

A

S3

B

2S3

C

4S3

D

None of these

Answer

S3

Explanation

Solution

S1 = n2\frac{n}{2} [2a + (n –1) d]

S2 = 2n2\frac{2n}{2} [2a + (2n –1) d]

S3 = 3n2\frac{3n}{2} [2a + (3n –1) d]

S2 –S1 =n2\frac{n}{2} [2a + d(3n –1)]

S2 – S1 = S33\frac{S_{3}}{3}

3(S2 – S1) = S3