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Let Sk be the sum of first k terms of an...

Let `S_k` be the sum of first `k` terms of an A.P. What must this progression be for the ratio `(S_(k x))/(S_x)` to be independent of `x ?`

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Let, `a_1` be the first term and d be common difference of an AP then
`S_n=n/2 [2a_1+(n-1)d]`
`=>S_x=x/2[2a_1+(x-1)d]`
`=>S_(kx)=(kx)/2[2a_1+(kx-1)d]`
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RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
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