Use the explicit formula to find a recursive formula for the sequence an. Write your answer in simplest form.The recursive formula should depend on an−1.an=−2n+29an=______
Q. Use the explicit formula to find a recursive formula for the sequence an. Write your answer in simplest form.The recursive formula should depend on an−1.an=−2n+29an=______
Identify Sequence Type: Identify if the given sequence is geometric or arithmetic.an=−2n+29 does not involve any exponent terms, which means it is not geometric. Since the formula involves a constant difference between terms (indicated by the linear term −2n), the sequence is arithmetic.
Find First Term: Find the first term of the sequence using the explicit formula.a1=−2(1)+29=−2+29=27This is the value of the sequence when n=1.
Find Second Term: Find the second term of the sequence using the explicit formula.a2=−2(2)+29=−4+29=25This is the value of the sequence when n=2.
Find Common Difference: Find the common difference in the arithmetic sequence.d=a2−a1=25−27=−2The common difference d is the amount by which each term decreases to get to the next term.
Write Recursive Formula: Write the recursive formula by plugging in the value of the common difference.Substitute −2 for d in an=a(n−1)+d. an=a(n−1)−2This recursive formula expresses each term of the sequence as the previous term minus 2.
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