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for an arthemetic progression S 2n =3S n then the value of S 3n /S n =??

for an arthemetic progression S2n=3Sn then the value of S3n/Sn=??

Grade:12th pass

1 Answers

Vikas TU
14149 Points
7 years ago
 S2n=3Sn
[n + (2a + (2n -1)d)] = [3n/2 + 6a + 3nd -3d]

after solving ,
 2a – d = -n/4 – nd/2.......................................(1)

S3n = [3n/2 + 2a + 3nd -d] 
after substituting from eqn. (1)
S3n = 5n/2[d+ 1/2]

and Sn = 2a – d + 2
nd + n 
after substituting rom eqn. (1)

= 3n/2[d + 1/2]
 
Hence, 
S3n/Sn = 5/3
 

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