Question

Find the indicated term of each arithmetic sequence.

$a_{43}$ for 5, 9, 13, 17, …

Short answer

The indicated term of the arithmetic sequence is173.

Step-by-step solution

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.