Find the indicated term of the arithmetic sequence with the given description.The first term is 3580, and the common difference is −16. Which term of the sequence is 2924?n =
Question
Find the indicated term of the arithmetic sequence with the given description.The first term is 3580, and the common difference is −16. Which term of the sequence is 2924?n =
Solution
To find the term number (n) of an arithmetic sequence, you can use the formula:
n = 1 + (a_n - a_1) / d
where:
- a_n is the term you're looking for (in this case, 2924),
- a_1 is the first term of the sequence (in this case, 3580), and
- d is the common difference (in this case, -16).
Substituting the given values into the formula, we get:
n = 1 + (2924 - 3580) / -16
Solving the equation step by step:
- Calculate the difference between a_n and a_1: 2924 - 3580 = -656
- Divide this difference by the common difference: -656 / -16 = 41
- Add 1 to the result: 1 + 41 = 42
So, the term number (n) of the sequence that is 2924 is 42.
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