If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of `p+q` terms will be

Explanation

Since
`S_n = n/2 [2a + (n - 1) d] `
for an A.P.
whose
first term = `a`,

common difference = `d`
number of terms = `n`.

∴ `S_p = q = p/2 (2a + (p – 1)d) `

⇒ `2q = 2ap + p (p – 1)d ...(i)`


Again ,

` S_q = p = q/2 (2a + (q – 1) d) `

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