Correct Answer - Option 2 : 33
Given:
The ratio of the third term to the fifth term of an AP series is 11 : 17.
The second term is 24.
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’.
T3/T5 = (a + 2d)/(a + 4d)
⇒ (a + 2d)/(a + 4d) = 11/17
⇒ 17a + 34d = 11a + 44d
⇒ 6a - 10d = 0 ----(1)
T2 = a + d = 24 (given) ----(2)
After Solving (1) and (2), we get
a = 15, d = 9
Third term T3 = a + 2d = 15 + 2 × 9 = 33
∴ Required answer is 33.