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Instructions: For the following sequence, state the common difference, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.Sequence: 32,24,16,8,โ€ฆ32,24,16,8,โ€ฆCommon Difference: Answer 1 Question 17an=40โˆ’8n๐‘Ž๐‘›=40โˆ’8๐‘›Answer 2 Question 17an=anโˆ’1โˆ’8๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ’8a1=32๐‘Ž1=32Answer 3 Question 17a25=๐‘Ž25= Answer 4 Question 17

Question

Instructions: For the following sequence, state the common difference, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.Sequence: 32,24,16,8,โ€ฆ32,24,16,8,โ€ฆCommon Difference: Answer 1 Question 17an=40โˆ’8n๐‘Ž๐‘›=40โˆ’8๐‘›Answer 2 Question 17an=anโˆ’1โˆ’8๐‘Ž๐‘›=๐‘Ž๐‘›โˆ’1โˆ’8a1=32๐‘Ž1=32Answer 3 Question 17a25=๐‘Ž25= Answer 4 Question 17

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Solution

The common difference of the sequence is -8. This is calculated by subtracting the second term from the first term (24 - 32 = -8).

The explicit form of the rule is an=40โˆ’8n. This form allows you to find the nth term without knowing the previous term.

The recursive form of the rule is an=anโˆ’1โˆ’8. This form allows you to find the nth term only if you know the (n-1)th term.

To find the 25th term (a25), you can use the explicit form of the rule. Substitute n=25 into the formula:

a25 = 40 - 8*25 = 40 - 200 = -160.

This problem has been solved

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