We have that the arithmetic sequence is referred to a sequence that the difference between the numbers is constant. While the geometric sequence is a sequence where each number after the first is identified by multiplying the previous one by a fixed number.
a) Given:
57, 61, 65...
The difference is given by:
[tex]\begin{gathered} 61-57=4 \\ 65-61=4 \end{gathered}[/tex]
The difference between the numbers is 4, that is, a constant number. Therefore, It's an arithmetic sequence.
Answer: arithmetic sequence
b) The formula for the arithmetic sequence is given by:
[tex]a_n=a_1+(n-1)d[/tex]
Substitute the values:
[tex]\begin{gathered} a_n=57+(n-1)4 \\ Simplify \\ a_n=57+4n-4=4n+53 \end{gathered}[/tex]
Answer:
[tex]a_n=4n+53[/tex]
c) For n = 9, we have:
[tex]a_9=4(9)+53=36+53=89[/tex]
Answer: he scores 89 in the 9th quiz.
