Use the explicit formula to find a recursive formula for the sequence a. Write your answer in simplest form.The recursive formula should depend on a.a=−17n+39a=______
Q. Use the explicit formula to find a recursive formula for the sequence a. Write your answer in simplest form.The recursive formula should depend on a.a=−17n+39a=______
Identify Sequence Type: Identify if the given sequence is geometric or arithmetic.The explicit formula a=−17n+39 involves a linear term in n, which suggests that the sequence is arithmetic, as it does not involve any exponent terms on n.
Find First Term: Find the first term of the sequence using the explicit formula.To find the first term, a1, we substitute n=1 into the explicit formula:a1=−17(1)+39a1=−17+39a1=22
Find Second Term: Find the second term of the sequence using the explicit formula.To find the second term, a2, we substitute n=2 into the explicit formula:a2=−17(2)+39a2=−34+39a2=5
Find Common Difference: Find the common difference in the arithmetic sequence.The common difference, d, is the difference between consecutive terms of the sequence:d=a2−a1d=5−22d=−17
Write Recursive Formula: Write the recursive formula by plugging in the value of the common difference.The recursive formula for an arithmetic sequence is given by an=a(n−1)+d. We substitute −17 for d to get the recursive formula:an=a(n−1)−17
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