Question

A child is creating a pyramid with building blocks. The top three levels include 3 blocks, 7 blocks, and 11 blocks. Part 1: How many blocks would be needed for a pyramid 25 levels tall? 2: Use complete sentences to explain how a sum of an arithmetic series was applied.

Answer 1

every level has 4 more then the one above, so by using this formula (3+0 X 4) (3+1 X 4) and so on i can see, i dont know where to go from here

Answer 2

What does n represent in your formula N=(3+4n)?
What would N be for n=1,2,...

Answer 3

@mathmate how come u adjust 25 in this formula

Answer 4

I am using the formula proposed by OP, and suggested some verifications to make adjustments, if required.

Answer 5

im not sure

Answer 6

does n = 25?

Answer 7

i guess sum is 25.not sure though.

Answer 8

The formula you proposed works like this:
when n=1, N=3+4(1)=7, which corresponds to the number of blocks for the second level, and
when n=2, N=3+4(2)=11, which corresponds to the third level.
If you want the formula to accept n as the level number, you will need to adjust it as follows:
N=3+4(n-1)=4n-1
Check N with this new formula for n=1,2 and 3 before you attempt the 25th level.

Answer 9

so the for a 25 level pyramid the bottom level would have 103 blocks? do i have to do this for all 25 levels or is there a formula/shortcut?

Answer 10

Did you check the formula for n=1,2 and 3?
If it worked for 1,2 and 3, chances are good that it works for 25 (directly).

Answer 11

it works for my original formula, the formula you mentioned is just a more complicated formula with more steps imo

Answer 12

this is an arithmetic series...
an = a1 + (n - 1)d
a25 = 3 + (25 - 1) * 4
a25 = 3 + 24 * 4
a25 = 3 + 96
a25 = 99 -- this is how many blocks that are on the 25th level

sn = n(a1 + an)/2
s25 = 25(3 + 99) / 2
s25 = 25(102) / 2
s25 = 2550/2
s25 = 1275 -- this is the sum of all blocks all the way to the 25th level