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=14n−23a=______
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=14n−23a=______
Identify Sequence Type: Identify if the given sequence is geometric or arithmetic.The explicit formula a=14n−23 involves a linear term in n without any exponents, which indicates that the sequence is arithmetic.
Find First Term: Find the first term of the sequence using the explicit formula.Substitute n=1 into the explicit formula to find the first term a1.a1=14(1)−23a1=14−23a1=−9
Find Second Term: Find the second term of the sequence using the explicit formula.Substitute n=2 into the explicit formula to find the second term a2.a2=14(2)−23a2=28−23a2=5
Find Common Difference: Find the common difference in the arithmetic sequence.The common difference d is the difference between any two consecutive terms.d=a2−a1d=5−(−9)d=5+9d=14
Write Recursive Formula: Write the recursive formula by plugging in the value of the common difference.The recursive formula for an arithmetic sequence is an=an−1+d.Substitute 14 for d in the recursive formula.an=an−1+14
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