Chapter 9.2, Problem 86E

To determine

To Explain: How to use first two terms of an AP to find the nth term

Explanation of Solution

Given: Explain how to use the first two terms of an arithmetic sequence to find the nth term .

The first two terms of the arithmetic sequence give us the common difference of the sequence

This value of common difference will put into the formula of nth term of an arithmetic sequence

For example

Let first term = 2

Second term = 4

N = 10

Then

Using the nth term formula

  $\begin{array}{l}{a}_1=2\\ a_2=4\\ n=10\\ d=a_2-a_1=4-2=2\\ a_n=a+(n-1)d\\ a_{10}=2+(10-1)2\\ a_{10}=2+9(2)\\ a_{10}=2+18\\ a_{10}=20\end{array}$

Therefore, The nth term in this example is 20