Q46. - Algebra 2

Question

Write an equation for the n^th term of each arithmetic sequence.

7, 16, 25, 34, ....

Step-by-Step Solution

Answer

An equation for the n^th term of the arithmetic sequence is $a_n=9n-2$  .

Step 1. Given Information.

Given arithmetic sequence is 7, 16, 25, 34, ....

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  $a_1=7$

The difference between the first two terms is   $16-7=9$

The difference between the next two terms is   $25-16=9$

Hence, the common difference is  $d=9$

 Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_n=7+(n-1)\left(9\right)\\ a_n=7+9n-9\\ a_n=9n-2\end{array}$

Step 3. Conclusion .

Hence, an equation for the n^th term of the arithmetic sequence is $a_n=9n-2$ .