Correct Answer - Option 2 : 96
Given:
The sum of third and tenth term of an A.P is 89. Second term is 13
Formula:
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’.
From the question
T3 + T10 = 89
⇒ (a + 2d) + (a + 9d) = 89
⇒ 2a + 11d = 89 ----(1)
And T2 = 13 (given)
⇒ a + d = 13 ----(2)
By solving equation (1) and (2) we get
89 - 11d = 26 – 2d
⇒ 9d = 63
d = 7 and a = 6
The sum of the sixth and the eighth terms = (a + 5d) + (a + 7d)
⇒ 2a + 12d
⇒ 2 × 6 + 12 × 7 = 12 + 84 = 96
∴ required answer is 96