Question

In Problems 1– 4, write down the first five terms of each sequence.

$$\begin{gathered} a_1=2 \\ {a}_n=2-a_{n-1} \end{gathered}$$

Short answer

The first five terms of the sequence are: $2,0,2,0,2$

Step-by-step solution

Given information.  

General term of the sequence:

$a_n=2-a_{n-1}$

First term of the sequence:$a_1=2$

Step 2. Substitute first four integral value of  n starting from 2 in the expression  anand solve. 

Second term:

$$\begin{gathered} a_2=2-a_{2-1} \\ =2-a_1 \\ =2-2 \\ =0 \end{gathered}$$

Third term:

$$\begin{gathered} a_3=2-a_{3-1} \\ =2-a_2 \\ =2-0 \\ =2 \end{gathered}$$

Fourth term:

$$\begin{gathered} a_4=2-a_{4-1} \\ =2-a_3 \\ =2-2 \\ =0 \end{gathered}$$

Fifth term:
$$\begin{gathered} a_5=2-a_{5-1} \\ =2-a_4 \\ =2-0 \\ =2 \end{gathered}$$

So, first five term of the sequence are:$2,0,2,0,2$