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What is the explicit formula for the arithmetic sequence 2,7,12,17

User Hi
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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.

User Vera
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