a The general equation of an arithmetic sequence can be written in the following format.
t(n)=mn+t(0)
In this equation m is the common difference, t(0) is the zeroth term, and n is the term number. The common difference is the difference between two consecutive terms. We can find this by examining the sequence.
The arithmetic sequence has a common difference of m= 4. With this information, we have half of what we need to complete the equation.
t(n)= 4n+t(0)
To find the zeroth term, we can substitute any of the three data points (1,- 23), (2,- 19), and (3,- 15) into the function and solve for t(0).
b By solving the inequality t(n)≥ 10 000 we can determine the number of times n the generator must be applied to make the result greater than 10 000.
Notice that n has to be an integer. Therefore, if n has to be greater than 2506.75, we must round our answer up to 2507.
...
t( 2506)=4( 2506)-27=9997
t( 2507)=4( 2507)-27=10 001
