a To determine if the sequence is arithmetic or geometric, we have to find out if there is a common difference or a common ratio between consecutive terms.
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= 12. Let's add this to the formula.
a_n=a_0( 1/2)^n
To find the zeroth term, we can, for example, substitute a_1= 12 in the formula and solve for a_0.
Now we can complete the equation.
a_n=1(1/2)^n ⇔ a_n=(1/2)^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= - 2.
a_n= - 2n+a_0
To find the zeroth term, we can, for example, substitute a_1=- 7.5 in the formula and solve for a_0.
