Question

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

$a_1=5$and$d=3$

Short answer

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

$5,8,11,14,17$

Step-by-step solution

Step 1. Given information

We have first term $a_1=5$and common difference $d=3$.

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

Step 2. Find the second term

First term is $5$.

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

Put $n=2$.

$$\begin{gathered} a_2=a_1+(2-1)3 \\ {a}_2=5+\left(1\right)3 \\ {a}_2=5+3 \\ {a}_2=8 \end{gathered}$$

Step 3. Find third term

Put $n=3$

$$\begin{gathered} a_3=a_1+(3-1)3 \\ {a}_3=5+\left(2\right)3 \\ {a}_3=5+6 \\ {a}_3=11 \end{gathered}$$

Step 4. Find fourth term

Put $n=4$.

$$\begin{gathered} a_4=a_1+(4-1)3 \\ {a}_4=5+\left(3\right)3 \\ {a}_4=5+9 \\ {a}_4=14 \end{gathered}$$

Step 5. Find fifth term

Put $n=5$.

$$\begin{gathered} a_5=a_1+(5-1)3 \\ {a}_5=5+\left(4\right)3 \\ {a}_5=5+12 \\ {a}_5=17 \end{gathered}$$