Answer:
An = 5n - 3.
Explanation:
The explicit formula for an arithmetic sequence is given by the formula:
An = A1 + (n - 1)d
Where:
- An is the nth term of the sequence.
- A1 is the first term of the sequence.
- n is the position of the term in the sequence.
- d is the common difference between consecutive terms.
In the arithmetic sequence 2, 7, 12, 17, the first term A1 is 2. We can observe that the common difference d between consecutive terms is 5. To find the explicit formula, we can substitute the values into the formula:
An = 2 + (n - 1)5
Simplifying this equation gives us the explicit formula for the given arithmetic sequence:
An = 5n - 3
For example:
- To find the 3rd term, we substitute n = 3 into the formula: A3 = 5(3) - 3 = 15 - 3 = 12.
- To find the 5th term, we substitute n = 5 into the formula: A5 = 5(5) - 3 = 25 - 3 = 22.
So, the explicit formula for the arithmetic sequence 2, 7, 12, 17 is An = 5n - 3.