Correct Answer - Option 4 : 49
Given:
The first term of an AP is 23. The ratio of the 10th term and the 11th term is 140 : 153.
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’.
a = 23 (given)
T10/T11 = (a + 9d)/(a + 10d) = 140/153
⇒ (23 + 9d)/(23 + 10d) = 140/153
⇒ (23 + 9d) × 153 = (23 + 10d) × 140
⇒ 3519 + 1377d = 3220 + 1400d
⇒ 23d = 299
∴ d = 13
Third term T3 = a + 2d
⇒ 23 + 2 × 13 = 23 + 26 = 49
∴ Required answer is 49.
