Question

The start of a quadratic sequence is shown below. Write down the nᵗʰ term rule for this sequence.

6, 9, 14, 21, 30, ...

Answer 1

The given quadratic sequence is: 6, 9, 14, 21, 30, ...

To find the nth term (\(a_n\)) rule for this sequence, we need to identify the differences between consecutive terms:

1. \(9 - 6 = 3\)

2. \(14 - 9 = 5\)

3. \(21 - 14 = 7\)

4. \(30 - 21 = 9\)

We observe that the differences are increasing by 2 each time. This indicates a quadratic relationship. The differences are consecutive odd numbers: 3, 5, 7, 9, ...

The nth term rule for the given quadratic sequence is then \( a_n = 6 + (n-1)(n+1) \).

You can verify this by substituting values for \(n\) and checking if you get the corresponding terms in the sequence.