Takuya's parents gave him $100dollar as a birthday gift. Since he loves board games, he spent $20dollar out of his present on board games at the end of each month until his money ran out. Let f(n) be the amount of money that remained from Takuya's present during month n, where n=1 represents the month he received his present.
f is a sequence. What kind of sequence is it?
p.s" tell me if it is a geometric sequence or arithmetic and find the explicit formula

The amount of money that remained from Takuya's presence during month n is expressed as an=120-20n and the sequence is an arithmetic sequence.

What is an arithmetic sequence?

The arithmetic sequence is the sequence where the common difference remains constant between any two successive terms. Let us recall what is a sequence. A sequence is a collection of numbers that follow a pattern. The general form of an arithmetic sequence is an=a+(n-1)d.

If Takuya's parents gave him $100 as a birthday gift and she spent $20 each month on board games until his money ran out, this means he keeps spending $20 every month and his money keeps reducing by the same amount each month until his money ran out, the following can be inferred;

initial amount = $100

If he spends $20 each month,

Balance at the end of 1st month = $100-$20 = $80

Balance at the end of 2nd month = $80-$20 = $60

Balance at the end of 3rd month = $60-$20 = $40 and so on

Since the amount keeps reducing by the same value i.e $20, then the sequence formed is an arithmetic sequence.

a is the first term of the sequence = 100

d is the common difference = 80-100 = 60-80 = 40-60 = -20

n is the number of terms

Substituting the given values in the formula we have; an=100+(n-1)(-20)

⇒an=100+(-20n+20)

⇒an=100-20n+20

⇒an=120-20n

Therefore, the amount of money that remained from Takuya's presence during month n is expressed as an=120-20n and the sequence is an arithmetic sequence.

To learn more about an arithmetic sequence visit:

https://brainly.com/question/12108818.

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