Multiple choice

How many terms are there in the sequence 3, 6, 9, 12, ... 111 ?

  1. 35

  2. 36

  3. 37

  4. 38
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C Correct answer
Explanation

This is an arithmetic progression with first term a=3 and common difference d=3. The nth term formula is a + (n-1)d = 111, so 3 + (n-1)3 = 111, which simplifies to (n-1)3 = 108, n-1 = 36, n = 37.

AI explanation

The sequence is an arithmetic progression with a first term of 3, a common difference of 3, and a last term of 111. Using the arithmetic progression term formula an = a + (n-1)d, we set up the equation 111 = 3 + (n-1)3. Subtracting 3 from 111 leaves 108 = (n-1)3, which means n-1 equals 36. Adding 1 to both sides gives the result of 37 terms.

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