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