After one customer buys 4 new tires, a garage recycling bin has 20 tires in it. After another customer buys 4 tires, the bin has 24 tires in it.


What is the explicit formula to represent the # of tires in the bin as an arithmetic sequence? And how many tires are in the bin after 9 customers buy all new tires?

Verified Answer :

its (24) 4×9=36. so (36 +24 =60) so there is 60 tires in the bin

Answer:

Arithmetic sequence formula is: \(a_n = 20 + (n - 1) \times 4\)

After 9 customers there are 52 tires in the bin

Step-by-step explanation:

The general arithmetic sequence formula is:

\(a_n = a_1 + (n - 1) \times d\)

where \(a_1\) is the first term, \(a_n\) is the nth term, n is the term position and d is the common difference.

Assuming \(a_1\) = 20

The second term is 24, then:

\(24 = 20 + (2 - 1) \times d\)

d = 24 - 20 = 4

So,  for this case, the arithmetic sequence formula is:

\(a_n = 20 + (n - 1) \times 4\)

With n = 9:

\(a_9 = 20 + (9 - 1) \times 4\)

\(a_9 = 52\)