Question

Given the sequence 9, 509, 1009, 1509, 2009 Determine its nth term

Answer 1

To find the nth term of the given sequence 9, 509, 1009, 1509, 2009, which increases by 500 at each step, use the arithmetic sequence formula nth term = a1 + (n - 1)d. Substituting the first term (9) and the common difference (500), the nth term is 500n - 491.

Step-by-step explanation:

The given sequence is 9, 509, 1009, 1509, 2009. To determine its nth term, we need to identify the pattern in the sequence. We can observe that each term increases by 500.

Step By Step Explanation :

1. Find the difference between consecutive terms: 509 - 9 = 500, 1009 - 509 = 500, and so on.
2. This indicates a common difference, suggesting the sequence is arithmetic.
3. The first term (a1) is 9, and the common difference (d) is 500. The nth term of an arithmetic sequence is given by: an = a1 + (n - 1)d.
4. Substitute the given values into the formula: nth term = 9 + (n - 1)×500.
5. Simplify the formula: nth term = 500n - 491.

Thus, the nth term of the given sequence is 500n - 491.