Q. 384.2( 5 Votes )

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.

Answer :

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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