Question

A pattern of dots is shown below. At each step, more dots are added to the pattern. The pattern continues indefinitely. How many dots would be found in the 30th step? Explain a rule that you could use to find the number of dots in any given step.

Answer 1

Using an arithmetic sequence, it is found that 89 dots would be found in the 30th step.

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

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

Researching the problem on the internet, it is found that the first step has 2 dots, the second has 5 dots, the third has 8 and so on, hence the first term is $a_1 = 2$ and the common difference is d = 3.

Then, the number of dots in the nth step is given by:

$a_n = 2 + 3(n - 1)$

In the 30th step, the number will be given by:

$a_{30} = 2 + 3(30 - 1) = 89$

More can be learned about arithmetic sequences at https://brainly.com/question/6561461