b A geometric sequence in first term form is written as t(n)=t(1)b^(n-1).
A
a t(n)=500+1500(n-1)
B
b t(n)=30(5)^(n-1)
Practice makes perfect
a An arithmetic sequence in first term form is is written in the following format.
t(n)=t(1)+m(n-1)
In this form, t(1) is the first term and m is the common difference. Examining the sequence, we see that the first term is 500. By measuring the difference between consecutive terms we can also determine the common difference.
Since we know that t(1)= 500 and m= 1500, we can write the equation in first term form.
t(n)= 500+ 1500(n-1)
b Like in Part B, we have to write the equation in first term form. However, by examining the sequence we see that this is a geometric sequence, which means a common ratio separates consecutive terms.
A geometric sequence in first term form is written in the following format.
t(n)=t(1)b^(n-1)
In this form t(1) is the first term and b is the common ratio. We have already determined the common ratio to b= 5. Examining the sequence, we can also identify the first term as t(1)= 30. If we substitute this into the first term form, we can write our equation.
t(n)= 30( 5)^(n-1)
