Q43. - Algebra 2

Question

Complete the statement for each arithmetic sequence.

 170 is the ___?__ term of -4, 2, 8, ... . 

Step-by-Step Solution

Answer

170 is the 30th term of the arithmetic sequence -4, 2, 8, … .

Step 1. Given Information.

Given arithmetic sequence is -4, 2, 8, ...

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  $a_1=-4$

The difference between the first two terms is  $2-(-4)=2+4=6$

The difference between the second two terms is  $8-2=6$

The common difference is  $d=6$

The given nth term is  $a_n=170$

 Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ 170=-4+(n-1)\left(6\right)\\ 170+4=(n-1)\left(6\right)\\ (n-1)\left(6\right)=174\\ n-1=\frac{174}{6}\\ n-1=29\\ n=29+1\\ n=30\end{array}$

Step 3. Conclusion .

Hence, 170 is the 30th term of the arithmetic sequence -4, 2, 8, … .