Question

An arrangement of bowling pins has 3 pins in the first row and 12 rows in all. In each successive row one pin is added.

What is the explicit rule for this situation, and how many pins will be in the 12th row?

Answer 1

The explicit rule for this situation is

`a_n = 2 + n`

In row 12 there will be 14 pins

Explanation:

We have an initial amount of 3 pins in the first row. Let's call the number of pins in row n.

where n is an integer and
`3\leq n\leq 12`.

So

`a_1 = 3`

In row n + 1 there will always be a pin more than in the previous row n, then:

`a_2 = a_1 +1`

Then:

`a_n = a_1 + (n-1)\\\\a_n = 3 + (n -1)\\\\a_n = 2 + n`

Finally in row 12 there will be:

`a_ {12} = 2 +12\\\\a_ {12} = 14\ pins`