Problem

17. The average attendance of a certain fitness class that meets daily for the first 4 days are given: 4,10,16,and 22 . Write a formula for the general term a_{n}that models the pattern.

Solution

Step 1 :The given sequence is \([4, 10, 16, 22]\).

Step 2 :This is an arithmetic sequence, where each term is obtained by adding a constant difference to the previous term.

Step 3 :The common difference can be obtained by subtracting the first term from the second term, or the second term from the third term, and so on.

Step 4 :In this case, the common difference is \(10 - 4 = 6\).

Step 5 :Once we have the common difference, we can write the general term \(a_{n}\) of the sequence.

Step 6 :The general term \(a_{n}\) of the sequence is given by \(a_{n} = 4 + (n-1)*6\).

Step 7 :\(\boxed{a_{n} = 4 + 6(n-1)}\) is the final answer.

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Source: https://solvelyapp.com/problems/40148/

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