Q44. - Algebra 2

Question

Complete the statement for each arithmetic sequence.

 124 is the ___?__ term of -2, 5, 12, ... . 

Step-by-Step Solution

Answer

124 is the 19th term of the arithmetic sequence -2, 5, 12, … .

Step 1. Given Information.

Given arithmetic sequence is -2, 5, 12, ...

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  $a_1=-2$

The difference between the first two terms is  $5-(-2)=5+2=7$

The difference between the second two terms is  $12-5=7$

The common difference is  $d=7$

The given nth term is  $a_n=124$

 Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ 124=-2+(n-1)\left(7\right)\\ 124+2=(n-1)\left(7\right)\\ (n-1)\left(7\right)=126\\ n-1=\frac{126}{7}\\ n-1=18\\ n=18+1\\ n=19\end{array}$

Step 3. Conclusion .

Hence, 124 is the 19th term of the arithmetic sequence -2, 5, 12, … .