Question

A child is creating a pyramid with building blocks. The top three levels include 4 blocks, 10 blocks, and 16 blocks. How many blocks would be needed for a pyramid 25 levels tall? Use complete sentences to explain how a sum of an arithmetic series was applied?

Answer 1

a1=4
a2=10
a3=16
an=a1+(n-1)d
here the common difference d=a2-a1=6
for 25 level, let's find the number of blocks
n=25
a25=a1+(25-1)*d
a25=4+24*6
a25=148
to find the total no. of blocks
we have to sum the number of blocks used in each level.
Sum of a arithmetic progression is given by=(n/2)*(a1+an)
(25/2)(a1+a25)
n=25
a1=4
a25=148
=25*(4+148)/2
25*152/2
Sum=1900 blocks for the pyramid

Answer 2

Thanks So Much :)