Answer:
Thus, the eleventh term is -25.
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
We are given the sequence:
5,2,-1,-4,...
We can directly find the common difference by subtracting two successive terms:
r = 2 - 5 = -3
The same result is obtained by subtracting any pair of successive terms.
The first term is a1 = 5. The general equation is:
[tex]a_n=5-3(n-1)[/tex]
[tex]a_n=5-3n+3[/tex]
[tex]a_n=-3n+8[/tex]
We need to find which term is -25, thus:
-3n + 8 = -25
Subtracting 8:
-3n = -25 - 8 = -33
Dividing by -3:
n = -33 / (-3)
n = 11
Thus, the eleventh term is -25.
