Question

In your own words, explain how the first two terms are used to find the tenth term. Show an example to illustrate your explanation.

Short answer

Find the common difference and then apply the nth term formula to find the 10th term.

Step-by-step solution

Step 1. Introduction.

First, find the difference between the first two terms and it will be a common difference (d) Now apply the formula for the nth term of the sequence to find the tenth term.

Step 2. Example of the question. 

Now, write an example.

$a_1=5,a_2=7$

Find the difference between the above number.

$\begin{array}{rcl}{a}_2-a_1& =& 7-5\\ & =& 2\end{array}$

Step 3. Find the 10th term.

Apply the arithmetic sequence formula to find the 10th term.

$\begin{array}{rcl}{a}_n& =& a_1+\left(n-1\right)d\\ a_{10}& =& 5+\left(10-1\right)2\\ & =& 5+18\\ & =& 23\end{array}$