Question

A clothing store is having a sale on T-shirts. The first T-shirt you buy costs \$7$7dollar sign, 7, and every additional shirt costs only \$5$5dollar sign, 5. Let f(n)f(n)f, left parenthesis, n, right parenthesis be the total cost of nnn shirts. fff is a sequence. What kind of sequence is it?

Answer 1

Answer:

Is an arithmetic sequence (see the explanation)

Step-by-step explanation:

The correct question is

The first T-shirt you buy costs $7, and every additional shirt costs only $5. Let f(n) be the total cost of n shirts. F is a sequence. What kind of sequence is it?

Let

f(n) ----> the total cost

n ---> the number of shirts

we know that

For n=1

$f(1)=7$

For n=2

$f(2)=7+5=12$

For n=3

$f(3)=7+5+5=f(2)+5=17$

For n=4

$f(4)=7+5+5+5=f(4)+5=22$

so

In general

$f(n)=f(1)+5(n-1)$

$f(n)=7+5(n-1)$

$f(n)=5n+2$

The sequence is

$7,12,17,22,27,...$

This is an arithmetic sequence, because it is a sequence of numbers in which the common difference between consecutive terms is 5