Question

Write a recursive sequence that represents the sequence defined by the following explicit formula: a_(n)=100((1)/(5))ⁿ⁻¹

Answer 1

To convert the explicit formula a_n = 100(1/5)^(n-1) to a recursive sequence, the initial term is a_1 = 100 and the recursive relationship is a_n = (1/5) * a_(n-1) for n > 1.

Step-by-step explanation:

To create a recursive sequence from the explicit formula an = 100(1/5)n-1, we need to define the starting term, a1, and establish a relationship between each term in the sequence and the previous term. The first term is given by the formula when n=1:

a1 = 100(1/5)1-1 = 100(1) = 100

For the recursive formula, we observe that each subsequent term is 1/5 times the previous term. Thus, for n > 1, we have:

an = (1/5) * an-1

Putting it all together, the recursive sequence is defined as follows:

• a1 = 100
• an = (1/5) * an-1, for n > 1