Answer:
[tex]a_n=-2-5n[/tex]
Step-by-step explanation:
Arithmetic Sequences
The arithmetic sequences are those where any term n 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]
Where
an = nth term
a1 = first term
r = common difference
n = number of the term
We are given the sequence
-7 -12 -17 -22 -27 ...
The first term of this sequence is a1=-7. We can calculate the common difference by subtracting two consecutive terms:
r = -12 - (-7) = -12 + 7 = -5
The nth term is:
[tex]a_n=-7+(n-1)(-5)[/tex]
Multiplying:
[tex]a_n=-7-5n+5[/tex]
Simplifying:
[tex]\boxed{a_n=-2-5n}[/tex]
