Q39. - Algebra 2

Question

Find the indicated term of each arithmetic sequence.

$a_{21}$  for 121, 118, 115, …

Step-by-Step Solution

Answer

The indicated term of the arithmetic sequence is 61.

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.