Answer:
[tex]a_n=6n-13[/tex]
Step-by-step explanation:
Arithmetic Sequences
The arithmetic sequences can be identified because each term is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.
The equation to calculate the nth term of an arithmetic sequence is:
[tex]a_n=a_1+(n-1)r[/tex]
Here a1 is the first term and r is the common difference.
The given sequence is:
[tex]a_1=-7, a_2=-1,a_3=5,a_4=11,...[/tex]
We can find the common difference by subtracting successive terms:
[tex]a_2-a_1=-1+7=6[/tex]
[tex]a_3-a_2=5+1=6[/tex]
[tex]a_4-a_3=11-5=6[/tex]
Since all the differences are equal, r=6. Thus, the general term is:
[tex]a_n=-7+6(n-1)[/tex]
Operating:
[tex]a_n=-7+6n-6[/tex]
[tex]a_n=6n-13[/tex]
The nth term is:
[tex]\mathbf{a_n=6n-13}[/tex]
