Multiple choice

Find the nth term of the given sequence. 3, 6, 11, 18, 27, …

  1. n2 + 1

  2. n2 + 6n + 2

  3. n2 + 2

  4. n2 + 3n + 1
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C Correct answer
Explanation

The sequence is 3, 6, 11, 18, 27. The differences are 3, 5, 7, 9. This is a quadratic sequence. For n=1, n^2+2 = 3. For n=2, 2^2+2 = 6. For n=3, 3^2+2 = 11. The formula n^2+2 fits all terms.

AI explanation

By examining the terms, we can see that each term is exactly 2 more than a perfect square. For the first term, 3 equals 1 squared plus 2; for the second term, 6 equals 2 squared plus 2; and for the third term, 11 equals 3 squared plus 2. Following this pattern, the formula for the nth term is n squared plus 2.

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