Q38. - Algebra 2

Question

Find the indicated term of each arithmetic sequence.

$a_{12}$  for 8, 3, -2, …

Step-by-Step Solution

Answer

The indicated term of the arithmetic sequence is -47.

Step 1. Given Information.

Given arithmetic sequence is 8, 3, -2, …

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  $a_1=8$

The difference between the first two terms is  $3-8=-5$

The difference between the next two terms is  $-2-3=-5$

The common difference is  $d=-5$

And the required term is  $n=12$

 Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{12}=8+(12-1)(-5)\\ a_{12}=8+\left(11\right)(-5)\\ a_{12}=8-55\\ a_{12}=-47\end{array}$

Step 3. Conclusion .

Hence, the indicated term of the arithmetic sequence is -47.