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
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: 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
Solution 1
The common difference of the sequence is 200. This is calculated by subtracting any term in the sequence from the term that follows it.
The explicit form of the rule is an = -198 + 200n. This form allows you to find the nth term of the sequence without knowing the previous term.
The recursive form of the rule is an = an-1 + 200. This form allows you to find the nth term of the sequence only if you know the (n-1)th term.
To find the 15th term of the sequence using the explicit form, substitute n = 15 into the explicit form of the rule: a15 = -198 + 200(15) = 2802.
Solution 2
The common difference in the sequence is 200. This is calculated by subtracting the first term from the second term (202-2 = 200).
The explicit form of the rule is an = -198 + 200n. This form allows you to find any term in the sequence without knowing the previous term.
The recursive form of the rule is an = an-1 + 200, a1 = 2. This form allows you to find any term in the sequence if you know the previous term.
To find the 15th term in the sequence using the explicit form, substitute n = 15 into the explicit form of the rule:
a15 = -198 + 200(15) = 2802.
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