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). 253, 248, 243, ... find the 43rd term.

Explanation:

Step1: Identify the sequence type

This is an arithmetic sequence since the difference between consecutive terms is constant. The common difference \(d\) is \(248 - 253=- 5\) (or \(243 - 248=-5\)).
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.

Step2: Substitute values into the formula

Here, \(a_{1} = 253\), \(d=-5\), and \(n = 43\).
Substitute these values into the formula:
\(a_{43}=253+(43 - 1)\times(-5)\)

Step3: Simplify the expression

First, calculate \(43 - 1 = 42\).
Then, calculate \(42\times(-5)=-210\).
Now, add this to \(253\): \(a_{43}=253-210 = 43\).

Answer:

\(43\)