Question

the first three terms of a sequence are given. write your answer as a decimal or whole number. round to the nearest thousandth (if necessary).
206, 202, 198, ...
find the 46th term.

Explanation:

Step1: Identify sequence type

This is an arithmetic sequence since the difference between consecutive terms is constant. The common difference \(d = 202 - 206 = -4\), and \(198 - 202 = -4\).

Step2: Recall arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1 + (n - 1)d\), where \(a_1\) is the first term, \(n\) is the term number, and \(d\) is the common difference.

Step3: Substitute values into formula

Here, \(a_1 = 206\), \(d = -4\), and \(n = 46\). Substitute these into the formula:

$$
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$$

Answer:

26