How do you find the nth term of 6, 12, 18, 24?

The nth term of the sequence 6, 12, 18, 24 is given by the formula 6n.

To find the nth term of a sequence, you need to identify a pattern or rule that the terms follow. In this sequence, each term increases by 6. This suggests that the sequence is arithmetic, where each term is obtained by adding a constant difference to the previous term. The first term (when n = 1) is 6, the second term (when n = 2) is 12, and so on.

To derive the formula, observe that the first term is 6, which can be written as 6 × 1. The second term is 12, which is 6 × 2. The third term is 18, which is 6 × 3, and the fourth term is 24, which is 6 × 4. This pattern shows that the nth term is 6 multiplied by n. Therefore, the nth term of the sequence can be expressed as 6n.

Using this formula, you can find any term in the sequence. For example, to find the 5th term, substitute n = 5 into the formula: 6 × 5 = 30. So, the 5th term is 30. This method works for any positive integer value of n, making it a powerful tool for analysing arithmetic sequences.