Question

PLEASE HELP!
A monument is built out of toothpicks. There are 35 rows and each row has six more toothpicks than the row above. The top row has five toothpicks.

Part 1: How many toothpicks are on the bottom row?

Part 2: Using complete sentences, explain the procedure taken to answer this question. (You don't have to type them out, please just explain your procedure and I'll take care of the sentences.)

Answer 1

this is an arithmetic sequence

so you know 1st term a = 5, common difference d= 6 and number of rows n = 35

so use

for the number in the bottom row


\[a_{35} = 5 + (35 -1) \times 6\]

Answer 2

well the pattern is
row Number 1 2 3 4 5 .....

tooth pick 5, 11, 17, 23, 29, ......

you can create an equation and and then substitute 35 to find the number of tooth pick in row 35

Answer 3

if I were to solve for \[a _{35}\] then I would end up getting 209 as my answer? is that right?

Answer 4

thats correct....

Answer 5

and if you create an equation from the table you get

t = 6r - 1

t = toothpicks and r = number of rows

so r = 35

t = 6(35) -1

Answer 6

wow, thank you so much! I actually understand it now. :)