Answer:
The 44th term is 23
Step-by-step explanation:
Arithmetic Sequences
The arithmetic sequences are identified because 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
If at least two consecutive terms are given, we can find the common difference by subtracting them.
We are given the terms 152, 149, 146,...
The common difference is
r = 149 - 152 = -3
The first term is a1=152.
Now we apply the general formula to find the term n=44
[tex]a_{44}=152-3(44-1)[/tex]
[tex]a_{44}=152-3(43)[/tex]
[tex]a_{44}=152-129=23[/tex]
The 44th term is 23
