Multiple choice

A sequence consists of 50 terms with 3rd term as 12 and last term as 106. Find the 29th term.

  1. 72

  2. 68

  3. 64

  4. 58
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C Correct answer
Explanation

Assuming an arithmetic progression: a + 2d = 12, a + 49d = 106. Subtracting gives 47d = 94, so d = 2. Then a = 12 - 4 = 8. The 29th term is a + 28d = 8 + 28(2) = 8 + 56 = 64.

AI explanation

The sequence is an arithmetic progression with the 3rd term as 12 and the 50th term as 106. Using the formula Tn = a + (n - 1)d, we get a + 2d = 12 and a + 49d = 106. Subtracting the first equation from the second gives 47d = 94, so d = 2; therefore, a = 8. Applying the formula for the 29th term, T29 = 8 + 28 * 2 = 64.

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