Q. Use the initial term and the recursive formula to find an explicit formula for the sequence a. Write your answer in simplest form. a=−7a=a+9a= ______
Given Sequence Type: We have:Initial term a1=−7Recursive formula: an=an−1+9Is the given sequence geometric or arithmetic?The recursive formula an=an−1+9 corresponds to an=an−1+d.Hence, the given sequence is arithmetic.
Common Difference: Recursive formula: an=an−1+9 Find the common difference in the arithmetic sequence. Compare an=an−1+9 with an=an−1+d to find d. So, d=9.
Explicit Formula: Explicit formula for arithmetic sequence:an=a1+d(n−1)Here, a1 is the first term, and d is the common difference. We have:a1=−7d=9Find the explicit formula.Substitute −7 for a1 and 9 for d in an=a1+d(n−1).a10a11a12a13Explicit formula is: a14
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