# The sum of third and tenth term of an A.P is 89. Find the sum of the sixth and the eighth terms of the progression if the second term is 13.

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The sum of third and tenth term of an A.P is 89. Find the sum of the sixth and the eighth terms of the progression if the second term is 13.
1. 100
2. 96
3. 94
4. 90

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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