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: 33,43,53,63,…33,43,53,63,…Common Difference: Answer 1 Question 11an=23+10n𝑎𝑛=23+10𝑛Answer 2 Question 11an=an−1+10𝑎𝑛=𝑎𝑛−1+10a1=𝑎1=Answer 3 Question 11Answer 4 Question 11a15=𝑎15= Answer 5 Question 11
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: 33,43,53,63,…33,43,53,63,…Common Difference: Answer 1 Question 11an=23+10n𝑎𝑛=23+10𝑛Answer 2 Question 11an=an−1+10𝑎𝑛=𝑎𝑛−1+10a1=𝑎1=Answer 3 Question 11Answer 4 Question 11a15=𝑎15= Answer 5 Question 11
Solution
The common difference in the sequence is 10. This is calculated by subtracting any term in the sequence from the term that follows it. For example, 43 - 33 = 10.
The explicit form of the rule is an = 23 + 10n. 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 + 10. This form allows you to find the nth term of the sequence only if you know the (n-1)th term.
The first term a1 in the sequence is 33.
To find the 15th term a15 in the sequence using the explicit form, substitute n = 15 into the explicit form of the rule: a15 = 23 + 10*15 = 173.
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