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?

The explicit rule for this situation is

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 .

So

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

Then:

Finally in row 12 there will be:

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

a

step-by-step explanation: