Problem 14 - College Algebra

Question

Write the first six terms of each arithmetic sequence. $$a_{n}=a_{n-1}-0.3, a_{1}=-1.7$$

Step-by-Step Solution

Answer

The first six terms of the arithmetic sequence are -1.7, -2.0, -2.3, -2.6, -2.9, and -3.2.

Step 1: Understand The Problem

The sequence is defined as \(a_{n}= a_{n-1} - 0.3\), where \(a_{1} = -1.7\). This means that each term is obtained by subtracting 0.3 from the previous term.

Step 2: Calculate the First Six Terms

Start with the given first term \(a_{1}=-1.7\), and subsequently calculate the next five terms using the defined rule. \[a_{2} = a_{1} - 0.3 = -1.7 - 0.3 = -2.0\] \[a_{3} = a_{2} - 0.3 = -2.0 - 0.3 = -2.3\] \[a_{4} = a_{3} - 0.3 = -2.3 - 0.3 = -2.6\] \[a_{5} = a_{4} - 0.3 = -2.6 - 0.3 = -2.9\] \[a_{6} = a_{5} - 0.3 = -2.9 - 0.3 = -3.2\]

Step 3: Present the First Six Terms

The first six terms of the sequence are \(a_{1} = -1.7\), \(a_{2} = -2.0\), \(a_{3} = -2.3\), \(a_{4} = -2.6\), \(a_{5} = -2.9\), and \(a_{6} = -3.2\).