Question

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

$a_1=-13$and$d=6$

Short answer

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

$-13,-7,-1,5,11$

Step-by-step solution

Step 1. Given information

We have first term $a_1=-13$and common difference $d=6$.

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

Step 2. Find the second term

First term is $-13$.

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

Put $n=2$.

$$\begin{gathered} a_2=a_1+(2-1)6 \\ {a}_2=-13+(2-1)6 \\ {a}_2=-13+6 \\ {a}_2=-7 \end{gathered}$$

Step 3. Find third term

Put $n=3$.

$$\begin{gathered} a_3=a_1+(3-1)6 \\ {a}_3=-13+(3-1)6 \\ {a}_3=-13+\left(2\right)6 \\ {a}_3=-13+12 \\ {a}_3=-1 \end{gathered}$$

Step 4. Find fourth term

Put $n=4$.

data-custom-editor="chemistry" $$\begin{gathered} a_4=a_1+(4-1)6 \\ {a}_4=-13+\left(3\right)6 \\ {a}_4=-13+18 \\ {a}_4=5 \end{gathered}$$

Step 5. Find fifth term

Put $n=5$.

$$\begin{gathered} a_5=a_1+(5-1)6 \\ {a}_5=-13+\left(4\right)6 \\ {a}_5=-13+24 \\ {a}_5=11 \end{gathered}$$