Answer:
There are 17 terms in the sequence
Step-by-step explanation:
Arithmetic Sequence
An arithmetic sequence is a list of numbers with a definite pattern by which each term is calculated by adding or subtracting a constant number called common difference to the previous term. If n is the number of the term, then:
[tex]a_n=a_1+(n-1)r[/tex]
Where an is the nth term, a1 is the first term, and r is the common difference.
In the problem at hand, we are given the first term a1=13, the last term an=-23, and the common difference r=-2 1/4. Let's solve the equation for n:
[tex]\displaystyle n=1+\frac{a_n-a_1}{r}[/tex]
We need to express r as an improper or proper fraction:
[tex]\displaystyle r=-2\frac{1}{4}=-2-\frac{1}{4}=-\frac{9}{4}[/tex]
Substituting:
[tex]\displaystyle n=1+\frac{-23-13}{-\frac{9}{4}}[/tex]
[tex]\displaystyle n=1+\frac{-36}{-\frac{9}{4}}[/tex]
[tex]\displaystyle n=1+36*\frac{4}{9}=17[/tex]
n=17
There are 17 terms in the sequence
