If the sum of n terms of two series in A.P. are in the ratio (5n + 4) : (9n + 6) then find the ratio of their 13th terms.  Choices
A) 129/139 B) 129/1378 C) 129/136 D) 129/134 E) 129/131
129/131xplanation:   Formula for sum of n terms in AP = SnSn = n2n2(2a + (n – 1)d ]   5n + 4 ⇒ 5(n – 1) + 9 ⇒ [2(92)+(n−1)5][2(92)+(n−1)5]   Common difference (d) = 5, First term (a) = 9292   Similarly   Second series given 9n + 6 ⇒⇒ 9(n – 1) + 15 ⇒ [2(152)+(n−1)9][2(152)+(n−1)9]   Common difference (d) = 9, First term (a) = 152152   So   13th term for first series is = a + 12d = 129/2   13th terms for second series is = a + 12d = 231/2   Ratio = 129/131   Answer:129/131
<result>E</result>
If the sum of n terms of two series in A.P. are in the ratio (5n + 4) : (9n + 6) then find the ratio of their 13th terms.