Answer:
Answer below
Step-by-step explanation:
Arithmetic Sequences
They can be identified because any term is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.
The formula 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
Suppose we know the 4th term (n=4) of a sequence is 25:
[tex]a_4=a_1+(4-1)r=25[/tex]
Simplifying:
a1 + 3r = 25
We can choose any combination of a1 and r to satisfy the equation above.
Solving for a1:
a1 = 25 - 3r
a)
Choosing r = 3:
a1 = 25 - 3*3 = 16
The sequence is:
16, 19, 22, 25, ...
And the term rule is:
[tex]a_n=16+3(n-1)[/tex]
Choosing r=8
a1 = 25 - 3*8 = 1
The sequence is:
1, 9, 17, 25, ...
The term rule is:
[tex]a_n=1+8(n-1)[/tex]
Choosing r=-10
a1 = 25 - 3*(-10) = 25 + 30 = 55
The sequence is:
55, 45, 35, 25, ...
The term rule is:
[tex]a_n=55-10(n-1)[/tex]
