Multiple choice

What is the nth term of the given sequence? 6, 9, 12, ...

  1. 3n

  2. 3n + 1

  3. 3n + 3

  4. 3n + 6
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C Correct answer
Explanation

The sequence is an arithmetic progression with first term a = 6 and common difference d = 3. The nth term is a + (n - 1)d = 6 + (n - 1)3 = 6 + 3n - 3 = 3n + 3.

AI explanation

To find the nth term of this sequence, we use the formula for an arithmetic progression, which is T = a + (n - 1)d. The first term a is 6 and the common difference d is 3, so we substitute these values into the formula to get T = 6 + (n - 1)3. Simplifying this expression yields T = 6 + 3n - 3, which further reduces to 3n + 3. The result is 3n + 3.

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