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= 110. Let's add this to the formula.
a_n=a_0( 1/10)^n
To find the zeroth term we can, for example, substitute a_1=100 in the formula and solve for a_0.
Now we can complete the equation.
a_n=1000(1/10)^n
b Like in Part A, we will first determine if this is a geometric or an arithmetic sequence.
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 determined that the common difference is m= - 50.
a_n= - 50n+a_0
To find the zeroth term we can, for example, substitute a_1=0 in the formula and solve for a_0.
