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If there are (2n+1)terms in an AP ,prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n
Ans: Let a, d be the I term & Cd of the AP.
∴ ak = a + (k - 1) d
s1 = sum to odd terms
s1 = a1 + a3 + ......... a 2n + 1
s1 = n +1/2 [a1 + a2 n +1 ]
= n + 1/2 [2a1 + 2nd]
s1 = (n + 1) (a + nd)
s2 = sum to even terms
s2 = a2 + a4 + ..... a 2n
s2 = n/2 [a2 + a2n ]
= n/2 [a + d + a + (2n - 1)d]
=n [a + nd]
∴ s1 : s2 = (n +1)(a + nd )/n(a + nd )
= n+1/n
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