Q40. - Algebra 2

Question

Find the indicated term of each arithmetic sequence.

 $a_{43}$  for 5, 9, 13, 17, …

Step-by-Step Solution

Answer

The indicated term of the arithmetic sequence is 173.

Step 1. Given Information.

Given arithmetic sequence is 5, 9, 13, 17, …

Step 2. Calculation .

The n^th term of an arithmetic sequence is given by $a_n=a_1+(n-1)d$ .

 

Here the first term is  $a_1=5$

The difference between the first two terms is  $9-5=4$

The difference between the next two terms is  $13-9=4$

The common difference is  $d=4$

And the required term is  $n=43$

 Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{43}=5+(43-1)\left(4\right)\\ a_{43}=5+\left(42\right)\left(4\right)\\ a_{43}=5+168\\ a_{43}=173\end{array}$

Step 3. Conclusion .

Hence, the indicated term of the arithmetic sequence is 173.