A child is creating a pyramid with building blocks. The top three levels include 5 blocks, 12 blocks, and 19 blocks.

Part 1: How many blocks would be needed for a pyramid 25 levels tall?

Part 2: Use complete sentences to explain how a sum of an arithmetic series was applied.

Question

A child is creating a pyramid with building blocks. The top three levels include 5 blocks, 12 blocks, and 19 blocks.

Part 1: How many blocks would be needed for a pyramid 25 levels tall? 

Part 2: Use complete sentences to explain how a sum of an arithmetic series was applied.

parthkohli · Answer

We have an arithmetic sequence: 5,12,19,26.... where d = 7.

parthkohli · Answer

Sum of an arithmetic sequence formula is applied, as the total number of blocks needed for $n$ levels is $5+12+19\cdots(\text{till }n \text{ terms})$

anonymous · Answer

uhu...

parthkohli · Answer

Did I confuse you? Sorry for that.

parthkohli · Answer

Firstly, do you see how creating each level increases the number of blocks by 7?

anonymous · Answer

no im just agreeing with you

parthkohli · Answer

Oh.

anonymous · Answer

n yes i understand so far

parthkohli · Answer

So can you use the formula?$$Sum~of~an~arithmetic~sequence = { n \over 2} \left(a_1 + a_n \right) $$

parthkohli · Answer

Here, the number of blocks(the number of terms) is 25. Substitute $n$ with 25.

parthkohli · Answer

Oh! And you have to find $a_{25}$ before continuing. For that, you must use the $n$th term in an arithmetic sequence formula.$$a_{25}= a_1 + (25 - 1)d $$We know that a1 = 5, d = 7, n = 25.$$a_{25}= 5  + 24\cdot 7  $$

anonymous · Answer

so a25=203

parthkohli · Answer

Yes. Now just find$${25 \over 2}(5 + 203)$$

anonymous · Answer

which is 2600

parthkohli · Answer

And that's it.

anonymous · Answer

thnxz ur a genius!