Question

Find the indicated term of each arithmetic sequence.

$a_{21}$for 121, 118, 115, …

Short answer

The indicated term of the arithmetic sequence is61.

Step-by-step solution

Step 1. Given Information.

Given arithmetic sequence is 121, 118, 115, …

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 $a_1=121$

The difference between the first two terms is $118-121=-3$

The difference between the next two terms is $115-118=-3$

The common difference is $d=-3$

And the required term is $n=21$

Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{21}=121+(21-1)(-3)\\ a_{21}=121+\left(20\right)(-3)\\ a_{21}=121-60\\ a_{21}=61\end{array}$

Step 3. Conclusion.

Hence, the indicated term of the arithmetic sequence is 61.