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.
Check: \(202 - 206 = -4\), \(198 - 202 = -4\), so common difference \(d=-4\), first term \(a_1 = 206\).

Step2: Use arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\).
We need to find the 46th term, so \(n = 46\), \(a_1 = 206\), \(d=-4\).

Step3: Substitute values into formula

Substitute into \(a_{46}=206+(46 - 1)\times(-4)\)
First, calculate \(46 - 1=45\)
Then, \(45\times(-4)=-180\)
Finally, \(a_{46}=206-180 = 26\)

Answer:

26