Question

sn denotes the sum of first n terms of AP..if S2n equal to 3Sn, then the ratio of S3n/Sn

Answer 1

We know that Sn = n(n+1)/2
now it is given that
S2n = 3Sn
⇒ 2n(2n+1)/2 = 3n(n+1)/2
⇒ 2(2n+1) = 3(n+1)
⇒ 4n+2 = 3n+3
⇒n = 1
then S3n/Sn = [3n(3n+1)/2]/[n(n+1)/2] = 3*4/1*2 = 6

hope u get the answer

Answer 2

Thank you for asking this question:

We know that Sn = n(n+1)/2

now it is given that

S2n = 3Sn

=> 2n(2n+1)/2 = 3n(n+1)/2

=> 2(2n+1) = 3(n+1)

=> 4n+2 = 3n+3

=> n = 1

then S3n/Sn = [3n(3n+1)/2]/[n(n+1)/2] = 3*4/1*2 = 6

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