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If in an A.P, Sn=n^2p and Sm=m^2p, then ...

If in an A.P, `S_n=n^2p` and `S_m=m^2p`, then `S_p` is equal to

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Let first term = a and Common difference = d
According to the question,
`Sn = n^2 p `
`Sn = n/2 (2a + (n–1) d) = n^2p `
`2a + (n–1) d = 2np….(1) `
And `Sm = m^2p `
`Sm= m/2 (2a + (m–1) d) = m^2p `
...
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