# If the number of terms of an A.P. be 2n + 3, then find the ratio of sum of the odd terms to the sum of even terms.

Given: Total number of terms = 2n + 3

Let the first term = a

and the common difference = d

Then, ak = a + (k – 1)d …(i)

Let S1 and S2 denote the sum of all odd terms and the sum of all even terms respectively.

Then,

S1 = a1 + a3 + a5 … + a2n+3

[using (i)]

= (n + 2)(a + nd + d) …(ii)

And, S2 = a2 + a4 + a6 … + a2n+2

[using (i)]

= (n+1)(a + nd + d) …(iii)

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