Question

Need to determine if sequence is arithmetic or geometric? See pic

Answer 1

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:

`\begin{gathered} 61-57=4 \\ 65-61=4 \end{gathered}`

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:

`a_n=a_1+(n-1)d`

Substitute the values:

`\begin{gathered} a_n=57+(n-1)4 \\ Simplify \\ a_n=57+4n-4=4n+53 \end{gathered}`

Answer:

`a_n=4n+53`

c) For n = 9, we have:

`a_9=4(9)+53=36+53=89`

Answer: he scores 89 in the 9th quiz.