Use the initial term and the recursive formula to find an explicit formula for the sequence a. Write your answer in simplest form. a=−35a=a−19a= ______
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=−35a=a−19a= ______
Given Sequence Type: We have:Initial term a1=−35Recursive formula: an=an−1−19Is the given sequence geometric or arithmetic?The recursive formula an=an−1−19 corresponds to an=an−1+d.Hence, the given sequence is arithmetic.
Common Difference: Recursive formula: an=an−1−19Find the common difference in the arithmetic sequence.Compare an=an−1−19 with an=an−1+d to find d.So, d=−19.
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=−35d=−19Find the explicit formula.Substitute −35 for a1 and −19 for d in an=a1+d(n−1).a10a11a12a13Explicit formula is: a14
More problems from Convert a recursive formula to an explicit formula