Use the initial term and the recursive formula to find an explicit formula for the sequence a. Write your answer in simplest form. a=−41a=a−11a= ______
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=−41a=a−11a= ______
Given Sequence Type: We have:Initial term a1=−41Recursive formula: an=an−1−11Is the given sequence geometric or arithmetic?The recursive formula an=an−1−11 corresponds to an=an−1+d.Hence, the given sequence is arithmetic.
Common Difference Calculation: Recursive formula: an=a(n−1)−11 Find the common difference in the arithmetic sequence. Compare an=a(n−1)−11 with an=a(n−1)+d to find d. So, d=−11.
Explicit Formula Derivation: 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=−41d=−11Find the explicit formula.Substitute −41 for a1 and −11 for d in an=a1+d(n−1).a10a11a12a13Explicit formula is: a14
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