If S1 be the sum of (2n + 1) terms of an A.P. and S2 sum of its odd terms, then prove that: S1: S2 = (2n + 1) : (n + 1).

To prove: S1: S2 = (2n + 1) : (n + 1)

we know that the sum of AP is given by the formula:



Substituting the values in the above equation



For the sum of odd terms, it is given by


s2 = a1 + a3 + a5 + …. a2n + 1


s2 = a + a + 2d + a + 4d + … + a + 2nd


s2 = (n + 1)a + n(n + 1)d


s2 = (n + 1) (a + nd)


Hence s1:s2


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