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?

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

Answer 1

what is the "constant" difference between numbers?

Answer 2

3,7,11.. indicates a arithmetic series. First term is 3. Common difference is 4.
From\[t = a + (n-1)d\]
t - n th term
a - first term
d - common difference
Find n for 25.
Now use
\[S = n/2 [2a + (n-1)d]\]
get the sum.

Answer 3

so i plug everything into the second equation?

Answer 4

yes

Answer 5

and my constant is 4 but idk how to use it

Answer 6

okay

Answer 7

in the order show by koushik_ksv

Answer 8

Yeah, once you got 'n' from the first.

Answer 9

what is a?

Answer 10

t - n th term
a - first term
d - common difference
Find n for 25.

Answer 11

I already mentioned, the first term.

Answer 12

I got 2[ 6+ (25-1)4] but dont know how to break it down

Answer 13

$$
\huge a_\color{red}{n} = a_1+(\color{red}{n}-1)\color{blue}{d}\\
\large {
\color{blue}{d}\text{ = common difference}\\
a_1\text{= term 1}\\
a_\color{red}{n}=n^{th}\text{ term}\\
\text{n = term you want, the }\color{red}{n}^{th}
}
$$

Answer 14

so what i got was wrong?