Question

A monument is built out of toothpicks. There are 30 rows and each row has seven more toothpicks than the row above. The top row has five toothpicks. How many toothpicks are on the bottom row? Using complete sentences, explain the procedure taken to answer this question.

Answer 1

I would start by identifying the first three rows of toothpicks:

5 + 0
5 + 1(7)
5 + 2(7)
.
.
.
What is the general equation you can make from this pattern?

Answer 2

5+a^n? @PhysicsGuru

Answer 3

nope there is no exponent in the series. what are the final two terms doing?

Answer 4

increasing? @PhysicsGuru

Answer 5

yes and what is the operation between the two add subtract divide or multiple?

Answer 6

add? @PhysicsGuru

Answer 7

nope 1(7) and 2(7) both of these terms of multiplying... you should notice that we are increasing the number in front of 7 by 1 with each new row so the general equation:

\[5 + n(7) \] where n is greater or equal to 0

Answer 8

so would i replace n with the row and then add the solutions together? @PhysicsGuru

Answer 9

yes

Answer 10

but the first row is n =0 the second is n =1 third n = 2 .... and so on

Answer 11

okay thank you!!! @PhysicsGuru