Question

If the sums of n terms of two arithmetic series are in the ratio 2n + 3 : 6n + 5, then the ratio between their 13th terms is

• A. (A) 53 : 155
• B. (B) 27 : 87
• C. (C) 29 : 83
• D. (D) 31 : 89

Answer 1

Answer: (A)

(A) 53 : 155

Answer 2

Explanation:
Given that the sum of n terms of two arithmetic series is in the ratio 2n+3:6n+5⇒(Sn)1(Sn)2=2n+36n+5where Sn be the sum of n terms of an arithmetic series. We know thatSn=n2[2a+(n−1)d]From Eq. (i), we get(Sn)1(Sn)2=n2[2a1+(n−1)d1]n2[2a2+(n−1)d2]=2n+36n+5⇒2a1+(n−1)d12a2+(n−1)d2=2n+36n+5∴2a1+(25−1)d12a2+(25−1)d2=53155⇒a1+12d1a2+12d2=53155⇒(T13)1(T13)2=53155