Multiple choice

How many terms are there in the sequence $9, 12, 15, ......66$?

  1. $18$
  2. $19$
  3. $20$
  4. $21$
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C Correct answer
Explanation

This is an arithmetic progression with a = 9, d = 3, l = 66. Formula: l = a + (n-1)d. 66 = 9 + (n-1)3. 57 = (n-1)3. 19 = n-1, so n = 20.

AI explanation

The sequence is an arithmetic progression with the first term a = 9, the common difference d = 3, and the last term l = 66. Using the nth term formula for an arithmetic progression, T_n = a + (n - 1)d, we substitute the known values to get 66 = 9 + (n - 1)3. Solving for n, we find 57 = (n - 1)3, which simplifies to 19 = n - 1, resulting in n = 20.

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