Correct Answer - Option 1 : 50
Given:
The 7th term of an AP is 71. The third term is 43.
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’.
T7 = a + (7 – 1)d
⇒ 71 = a + 6d ----(1)
T3 = a + (3 – 1)d
⇒ 43 = a + 2d ----(2)
From equation from (1) and (2)
71 – 6d = 43 – 2d
⇒ 4d = 28
⇒ d = 7
And a = 29
Fourth term, T4 = a + 3d
⇒ 29 + 3 × 7 = 50
∴ required answer is 50.