Question

consider the sequence whose first five terms are shown: 96, 24, 6, 1.5, 0.375, ... first, classify the sequence. then, describe the sequence and calculate the next two terms. 1. classify is each term equal to the previous term plus or minus the same number? (optional tab) is each term equal to the previous term multiplied or divided by the same non - zero constant? (optional tab) is each term equal to the sum of the previous two terms? (optional tab) is each term equal to the previous term plus a regularly increasing amount? (optional tab) you may use the optional tabs above to help you classify the sequence.

Explanation:

Step1: Find the common - ratio

We are given the sequence \(1.5,0.375,\cdots\). To check if it is a geometric sequence (where each term is equal to the previous term multiplied or divided by the same non - zero constant), we find the ratio of consecutive terms. Let \(a_1 = 1.5\) and \(a_2=0.375\). The common ratio \(r=\frac{a_2}{a_1}=\frac{0.375}{1.5}=0.25\).

Step2: Calculate the next two terms

The formula for the \(n\)th term of a geometric sequence is \(a_n=a_1r^{n - 1}\). The next term (\(n = 3\)) is \(a_3=a_2\times r=0.375\times0.25 = 0.09375\). The term after that (\(n = 4\)) is \(a_4=a_3\times r=0.09375\times0.25=0.0234375\).

Answer:

The sequence is a geometric sequence. The next two terms are \(0.09375\) and \(0.0234375\).