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.

129231129231

1212

23152315

None of the above

Explanation:

Formula for sum of n terms in AP = SnSn = n2(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

13th term for first series is = a + 12d = 12921292

13th terms for second series is = a + 12d = 23122312

Ratio = 129231