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The ratio of the third term to the fifth term of an AP series is 11 : 17. The second term is 24. Find the third term.
1. 22
2. 33
3. 44
4. 39

1 Answer

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Correct Answer - Option 2 : 33

Given:

The ratio of the third term to the fifth term of an AP series is 11 : 17.

The second term is 24.

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’.

T3/T5 = (a + 2d)/(a + 4d)

⇒ (a + 2d)/(a + 4d) = 11/17

⇒ 17a + 34d = 11a + 44d

⇒ 6a - 10d = 0                  ----(1)

T2 = a + d = 24 (given)      ----(2)

After Solving (1) and (2), we get

a = 15, d = 9

Third term T3 = a + 2d = 15 + 2 × 9 = 33

∴ Required answer is 33.

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