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
So
13th term for first series is = a + 12d = 12921292
13th terms for second series is = a + 12d = 23122312
Ratio = 129231