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.

Question

lgbasallote · Answer

procedure taken -> set-up toothpicks

zepp · Answer

I would be an arithmetic series, from top, you'll have 5, 5+7, 5+2*7+5+3*7 etc etc

zepp · Answer

It*

anonymous · Answer

yea but I got 208, is that right?

zepp · Answer

To find any term in an arithmetic series, you'll use the formula $a_{n} = a_{1}+(n+1)d$
Since we do not have to first term, we'll work backward.

$\huge  5 = a_{1}+(30+1)(-7)$
We have here $a_{30}$ = 5, 30th term, common difference being -7.
$\huge  5 = a_{1}+217$
$\huge a_{1} = 222$

anonymous · Answer

but u have a a1, its 5

anonymous · Answer

a1 = 5, n = 30, and d = 7, right?

zepp · Answer

Nuh-uh, 5 is the last term, you have 30 row and 5 is the top row
mean that
...,...,...,...,...,...,...,...,...,..., (29 terms later),  5

zepp · Answer

You can work that way, too, I think.

anonymous · Answer

but it says top row, which means the first row, right?

zepp · Answer

Uhhh, you are right :O

anonymous · Answer

really? s its 208?

zepp · Answer

So yes top row, first term = 5
Common difference +7
We are looking for the 30th term
a30 = 5+(30+1)7
a30 = 222

If would still be 222 :P

anonymous · Answer

its minus, the formula is an = a1 + (n - 1)d and the the 30 is what we are trying to find because of the last, 30th row... right?

zepp · Answer

Right, oh yeah, the minus >.>

So yes, your answer would be 208
(omg so misleading people today lol)

anonymous · Answer

haha its okay, thank u so much for talking it through with me! :)

zepp · Answer

Haha, no problem :)