Correct Answer - Option 2 : 9 : 11
Given:
In an AP, the ratio of the fifth term to the eleventh term is 2 : 3. The sixth term is 13.
Formula used:
nth term of an AP, Tn = a + (n - 1)d,
where ‘a’ is the first term, ‘n’ is the total number of terms and ‘d’ is the common difference.
Calculation:
Let the first term is ‘a’ and common difference is ‘d’.
According to question
T5/T11 = 2/3
⇒ (a + 4d)/(a + 10d) = 2/3
⇒ 3a + 12d = 2a + 20d
⇒ a – 8d = 0 ----(1)
And T6 = 13 (given)
⇒ a + 5d = 13 ----(2)
Solving equation (1) and (2)
8d + 5d = 13
⇒ 13d = 13
⇒ d = 1
and by putting value d = 1 in equation (1) we get,
a = 8
The ratio of the eleventh term and the fifteenth term = (a + 10d)/(a + 14d)
⇒ (8 + 10 × 1)/(8 + 14 × 1)
⇒ 18/22
∴ required answer is 9/11.