Question

sn denotes the sum of first n terms of AP..if S2n equal to 3Sn, then the ratio of S3n/Sn
answer is 6 solve step by step please​

Answer 1

Step-by-step explanation:

S2n = 3Sn

2n/2 { 2a + (2n-1)d } = 3n/2 { 2a + (n-1)d }

2n { 2a + (2n-1)d } = 3n { 2a + (n - 1)d }

4an + 4n²d - 2nd = 6an + 3n²d - 3nd

2an - n²d - nd = 0

n { 2a - nd - d } = 0

2a - (n + 1)d = 0

2a = (n + 1)d -------(1)

Now , S3n / Sn

3n/2 { 2a + (3n - 1)d } / n/2 { 2a + (n - 1)d }

3 { (n + 1)d + (3n - 1)d} / { (n + 1)d + (n - 1)d }

3 { d(n + 1 + 3n - 1) } / d { n + 1 + n - 1 }

3 d ( 4n ) / d ( 2n )

3(4n) / 2n

3 × 2

= 6

I hope it will help you