Question

In the following exercises, write the first five terms of each arithmetic sequence with the given first term and common difference.

$a_1=8$and$d=-2$

Short answer

We get the first five terms of the sequence as following:

$8,6,4,2,0$

Step-by-step solution

Step 1. Given information

We have first term $a_1=8$and common difference $d=-2$.

We have to write the first five terms of this arithmetic sequence.

Step 2. Find the second term

First term is $8$.

Formula for $n^{th}$term is $a_n=a_1+(n-1)d$.

Put $n=2$.

$$\begin{gathered} a_2=a_1+(2-1)(-2) \\ {a}_2=8+\left(1\right)(-2) \\ {a}_2=8-2 \\ {a}_2=6 \end{gathered}$$

Step 3. Find third term

Put $n=3$.

$$\begin{gathered} a_3=a_1+(3-1)(-2) \\ {a}_3=8+\left(2\right)(-2) \\ {a}_3=8-4 \\ {a}_3=4 \end{gathered}$$

Step 4. Find fourth term

Put $n=4$.

$$\begin{gathered} a_4=a_1+(4-1)(-2) \\ {a}_4=8+\left(3\right)(-2) \\ {a}_4=8-6 \\ {a}_4=2 \end{gathered}$$

Step 5. Find fifth term

Put $n=5$.

$$\begin{gathered} a_5=a_1+(5-1)(-2) \\ {a}_5=8+\left(4\right)(-2) \\ {a}_5=8-8 \\ {a}_5=0 \end{gathered}$$