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,…32,24,16,8,…Common Difference: Answer 1 Question 17an=40−8n𝑎𝑛=40−8𝑛Answer 2 Question 17an=an−1−8𝑎𝑛=𝑎𝑛−1−8a1=32𝑎1=32Answer 3 Question 17a25=𝑎25= 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,…32,24,16,8,…Common Difference: Answer 1 Question 17an=40−8n𝑎𝑛=40−8𝑛Answer 2 Question 17an=an−1−8𝑎𝑛=𝑎𝑛−1−8a1=32𝑎1=32Answer 3 Question 17a25=𝑎25= 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=40−8n. This form allows you to find the nth term without knowing the previous term.
The recursive form of the rule is an=an−1−8. 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.
Similar Questions
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: 2,202,402,602,…2,202,402,602,…Common Difference: Answer 1 Question 10an=−198+200n𝑎𝑛=−198+200𝑛Answer 2 Question 10an=an−1+200𝑎𝑛=𝑎𝑛−1+200a1=2𝑎1=2Answer 3 Question 10a15=𝑎15= Answer 4 Question 10
Instructions: For the following sequence, state the common ratio, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.Sequence: 3,6,12,24…3,6,12,24…Find: a9𝑎9Common Ratio: Answer 1 Question 2an=3⋅(2)n−1𝑎𝑛=3⋅(2)𝑛−1Answer 2 Question 2an=an−1⋅2𝑎𝑛=𝑎𝑛−1⋅2a1=3𝑎1=3Answer 3 Question 2a9=𝑎9= Answer 4 Question 2
Instructions: Identify the type of sequence and write the recursive rule. Sequence: 3,18,108,648,…3,18,108,648,…Type: Answer 1 Question 3an=an−1𝑎𝑛=𝑎𝑛−1 Answer 2 Question 3 Answer 3 Question 3a1=𝑎1= Answer 4 Question 3
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: 2,202,402,602,…2,202,402,602,…Common Difference: Answer 1 Question 10
Instructions: Identify the type of sequence and write the recursive rule. Sequence: −1,−2,−4,−8,…−1,−2,−4,−8,…Type: Answer 1 Question 8an=an−1𝑎𝑛=𝑎𝑛−1 Answer 2 Question 8 Answer 3 Question 8a1=𝑎1= Answer 4 Question 8
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.