Question

Find the indicated term of each arithmetic sequence.

$a_1=5,d=\frac{1}{3},n=12$

Short answer

The indicated term of the arithmetic sequence is$\frac{26}{3}$ .

Step-by-step solution

Step 1. Given Information.

Given indicated term of arithmetic sequence is $a_1=5,d=\frac{1}{3},n=12$

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 common difference is $d=\frac{1}{3}$$d=\frac{1}{3}$

And the required term is $n=12$

Plugging the values in the formula:

localid="1648552814070" $\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{12}=5+(12-1)\left(\frac{1}{3}\right)\\ a_{12}=5+\left(11\right)\left(\frac{1}{3}\right)\\ a_{12}=5+\frac{11}{3}\\ a_{12}=\frac{26}{3}\end{array}$

Step 3. Conclusion.

Hence, the indicated term of the arithmetic sequence is$\frac{26}{3}$.