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.

Answer 1

Answer:

The explicit rule for this situation is

$a_n = 2 + n$

In row 12 there will be 14 pins

Step-by-step 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:

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