Q37. - Algebra 2

Question

Find the indicated term of each arithmetic sequence.

$a_{12}$  for -17, -13, -9, …

Step-by-Step Solution

Answer

The indicated term of the arithmetic sequence is 27.

Step 1. Given Information.

Given arithmetic sequence is -17, -13, -9, …

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  $a_1=-17$

The difference between the first two terms is  $(-13)-(-17)=-13+17=4$

The difference between the next two terms is  $(-9)-(-13)=-9+13=4$

The common difference is  $d=4$

And the required term is  $n=12$

 Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{12}=-17+(12-1)\left(4\right)\\ a_{12}=-17+\left(11\right)\left(4\right)\\ a_{12}=-17+44\\ a_{12}=27\end{array}$

Step 3. Conclusion .

Hence, the indicated term of the arithmetic sequence is 27.