Instructions: Given one form of a sequence, write the other form. Recursivean=an−1⋅−3𝑎𝑛=𝑎𝑛−1⋅−3a1=2𝑎1=2Explicit Forman=𝑎𝑛= Answer 1 Question 7 (( Answer 2 Question 7 )n−1
Question
Instructions: Given one form of a sequence, write the other form. Recursivean=an−1⋅−3𝑎𝑛=𝑎𝑛−1⋅−3a1=2𝑎1=2Explicit Forman=𝑎𝑛= Answer 1 Question 7 (( Answer 2 Question 7 )n−1
Solution
The given sequence is in recursive form: an = an-1 * -3, with a1 = 2.
To find the explicit form, we need to understand how the sequence progresses.
The first term a1 is given as 2. The second term a2 would be a1 * -3 = 2 * -3 = -6. The third term a3 would be a2 * -3 = -6 * -3 = 18, and so on.
We can see that each term is the previous term multiplied by -3. This is a geometric sequence, where each term is the previous term multiplied by a constant ratio.
The explicit form of a geometric sequence is given by an = a1 * r^(n-1), where a1 is the first term, r is the ratio, and n is the term number.
In this case, a1 = 2, r = -3, and n is the term number.
So, the explicit form of the sequence is an = 2 * (-3)^(n-1).
Similar Questions
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
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: 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
Instructions: Write the recursive rule. Sequence: −11,−3,5,13,…−11,−3,5,13,…an=an−1𝑎𝑛=𝑎𝑛−1 Answer 1 Question 12 Answer 2 Question 12a1=𝑎1= Answer 3 Question 12
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
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.