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, T_{n }= 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

T_{3 }+ T_{10} = 89

⇒ (a + 2d) + (a + 9d) = 89

⇒ 2a + 11d = 89 ----(1)

And T_{2 }= 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**