The Smith family wants to build a human pyramid when they go to the beach this summer. They will put one person on top and add 2 more people for each descending row.

a.How many people will be in the seventh row?

b.Find the total number of people in a pyramid with seven rows.

c.Next summer, Jane Smith wants to build a pyramid with only the great-grandchildren. If they build it the same way, how many children are needed to make a pyramid with 10 rows?

d.Suppose the cast of The Simpsons built a pyramid in which the bottom row had 37 people, and they added 4 people between consecutive rows. How many rows tall is their pyramid?

e.What is the total number of people in the Simpson’s pyramid described in part d?

A. It's a trick question, if there is two people per row excluding the very top, then there should only be two in the seventh row.

B. there would be 15 total people in the seventh row.

If it's 1 person on top and 2 people each row, that would be 1+2(x)

1+2(x)
1+2(7)
1+14
=15

C. If it's the same way then we would just use the same equation.

1+2(x)
1+2(10)
1+20
=21

There would be a total of 21 people in the pyramid.

D. We would just need to subtract 4 from 37 repeatedly to find how many rows.

I did the math and it is 10 people since we can't have half a person.

E. If the bottom row has 37 and we know that it is 4 people up each time, and there are a total of 10 rows roughly, then we can safely assume there are 40 people + the bottom row 37 which is 77 people total.

I know I may not be right, but I hope this helps.

- Kathryn Irene