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Let Sn denote the sum of first n terms o...

Let `S_n` denote the sum of first n terms of an AP and `3S_n=S_(2n)` What is `S_(3n):S_n` equal to? What is `S_(3n):S_(2n)` equal to?

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`S_n=n/2[2a+(n-1)d]`
`3S_n=S_(2n)`
`3(n/2)[2a+(n-1)d]=(2n)/2[2a+(2n-1)d]`
`3/2[2a+(n-1)d]=2a+(2n-1)d`
`3a+3/2nd-3/2d=2a+2nd-d`
`a=(nd)/2+d/2`
`a=(n+1)d/2`
`2a=(n+1)d`
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