We have a common difference between consecutive terms, which means this is an arithmetic sequence. The formula for an arithmetic sequence follows a certain format.
a_n= mn+a_0
In the formula n is the term number, m is the common difference, and a_0 is the zeroth term. We have already determined that the common difference is m= 1500.
a_n= 1500n+a_0
To find the zeroth term we can, for example, substitute a_1=500 in the formula and solve for a_0.
Now we can complete the equation.
a_n=1500n+(- 1000) ⇔ a_n=1500n-1000
b Like in Part A, we will first determine if this is a geometric or an arithmetic sequence.
We have a common ratio between consecutive terms which means this is a geometric sequence. The formula for a geometric sequence follows a certain format.
a_n=a_0( b)^n
In the formula n is the term number, b is the common ratio, and a_0 is the zeroth term. We have already determined that the common ratio is b= 5.
a_n=a_0( 5)^n
To find the zeroth term we can, for example, substitute a_1=30 in the formula and solve for a_0.
