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,โฆ32,24,16,8,โฆCommon Difference: Answer 1 Question 17an=40โ8n๐๐=40โ8๐Answer 2 Question 17an=anโ1โ8๐๐=๐๐โ1โ8a1=32๐1=32Answer 3 Question 17a25=๐25= 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,โฆ32,24,16,8,โฆCommon Difference: Answer 1 Question 17an=40โ8n๐๐=40โ8๐Answer 2 Question 17an=anโ1โ8๐๐=๐๐โ1โ8a1=32๐1=32Answer 3 Question 17a25=๐25= Answer 4 Question 17
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=40โ8n. This form allows you to find the nth term without knowing the previous term.
The recursive form of the rule is an=anโ1โ8. 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.
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