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| 1. |
Let Sn denotes the sum of n terms of an A.P. if S2n =3Sn , the ratio S3n / sn= |
| Answer» Let 1st term be a and common difference be d.Given, S2n\xa0= 3sn{tex}\\therefore{/tex}\xa0{tex}\\frac { 2 n } { 2 }{/tex}\xa0[2a + (2n - 1) d] = 3 {{tex}\\frac { n } { 2 }{/tex}\xa0[2a + (n - 1) d]}{tex}\\Rightarrow{/tex}\xa04a + (4n - 2) d = 6a + (3n - 3)d{tex}\\Rightarrow{/tex}\xa02a = (n + 1)d\xa0...(i)Now,\xa0{tex}\\frac { S _ { 3 n } } { S _ { n } } = \\frac { \\frac { 3 n } { 2 } [ 2 a + ( 3 n - 1 ) d ] } { \\frac { n } { 2 } [ 2 a + ( n - 1 ) d ] }{/tex}=\xa0{tex}\\frac { 3 \\{ ( n + 1 ) d + ( 3 n - 1 ) d \\} } { ( n + 1 ) d + ( n - 1 ) d }{/tex}\xa0[from Eq. (i)]=\xa0{tex}\\frac { 3 ( 4 n d ) } { 2 n d }{/tex} = 6:1 | |