Question

A monument is built out of toothpicks. There are 25 rows and each row has eight more toothpicks than the row above. The top row has five toothpicks.
How many toothpicks are on the bottom row?

Answer 1

naming the top row as the first row, and the bottommost as the 25th row.

Since row 1 has 5 toothpicks.
row 2 has 5+8 = 13
row 3...


instead of just listing on and on, just derive a formula.

No. of toothpicks in nth row = 5 + (n-1)*8

Then solve accordingly, ( i will cut short my work as michael guides you along)

Answer 2

thats extremely completcated? your useing subscripts and all i need an easier example

Answer 3

hi, to try and solve it simply. Think of the top row as being = 5 + (0 x 8) and the second row as being = 5 + (1 x 8) ... if you keep going you can see that there are 25 rows and so they will keep increasing until the bottom row will be = 5 + (24 x 8) and that should give you your answer. Why isn't the bottom row = 5 + (25 X 8)? well thats because you only start adding the 8's from the second row

Answer 4

I'm sorry, I thought you needed the total number of toothpicks in the monument. My mistake.

The number of toothpicks in a row is achieved with \[5 + (n - 1)( 8)\] where n is the number of rows.

Answer 5

so would n equal 36?

Answer 6

no, he was using n to stand for the row that you wanted to find the answer for so, if you want to find answer on 25th row then use his equation and put 25 instead of n ie 5+ (25-1) x (8) = your answer. it is done this way so that if you wanted to find the number of toothpicks on the 17th row you could get that too, just by replacing n with 17 :)

Answer 7

197? i got 197

Answer 8

Yupeeee!
From @Mattd's instruction: 5+ (25-1) x (8) = your answer
It's arithmetic sequence with:
a1 = 5, n = 25, d = 8
=> a_25 = a_1 + 24 * d = .... = 197