b Is this geometric or arithmetic? What separates consecutive terms?
A
a t(n)=10(0.25)^(n-1)
B
b t(n)=-6n+4
Practice makes perfect
a The sequence can be either arithmetic or geometric. The difference between these sequences lies in the separation of consecutive terms.
Arithmetic: &Constant difference
&between consecutive terms
Geometric: &Constant factor
&between consecutive terms
Let's first try if it is an arithmetic sequence.
As we can see, we do not have a constant difference between consecutive terms which means it's not arithmetic. Let's try if its geometric.
We have a constant factor between consecutive terms and therefore this is a geometric sequence. A geometric sequence and can be written in the following format.
&t(n)=t(1)r^(n-1) [0.3em]
&r=common factor
&t(1)=first term
We know that the common factor is r= 0.25 and the first term is t(1)= 10. With this information, we can write the equation.
t(n)= 10( 0.25)^(n-1)
b Like in Part A, we first have to investigate if it is an arithmetic or a geometric sequence.
The constant difference between consecutive terms is -6. Therefore, this is an arithmetic sequence and can be written in the following format.
&t(n)=d(n-1) + t(1) [0.3em]
&d=common difference
&t(1)=first term
Let's substitute the common difference and first term into the equation.
