Question

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?

Answer 1

f(n) = 2 + 5n. This is an arithmetic sequence.

Explanation:

f(1) = 7

f(2) = 7 + 5

f(3) = 7 + 5 + 5 = 7 +10

f(4) = 7 + 5 + 5 + 5 = 7 + 15

In general,

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

= 7 + 5n - 5

= 2 + 5n

We have the sequence 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.