Okay. I'm feeling kinda dumb right now cuz i should know this but i don't. I actually know how to get the anwser...but i need and expression. (Algebra)
Okay, Their is a set of stairs made up of blocks. For three steps, its 6 blocks. The question is asking how many i would need for a 20 step staircase, and i could draw it out...but i don't want to do it that way. I'm trying to get and expression. When i put in into an Output Inpout chart, i see that the output numbers increse by one each time...but i don't know what to do after that!
Could somebody please help me a.s.a.p!
Thanks.......i'm still working on it. Sry for any spelling or grammar that is really bad---i was in a rush!
step(1) = 1
step(2) = 3
step (3) = 6
..
..
step(n) = n(n+1)/2
so step(20) = 20(21)/2 = 210
No problem! Let me help you out with that. To find an expression for the number of blocks needed for a given number of steps, let's analyze the pattern.
You mentioned that for three steps, six blocks are needed. Let's break it down further:
- For one step, two blocks are needed.
- For two steps, four blocks are needed.
- For three steps, six blocks are needed.
From this pattern, we can observe that the number of blocks needed is increasing by two each time (2, 4, 6).
To find the expression, we can represent the number of steps as 'n' and the number of blocks as 'b'.
We can see that when n = 1, b = 2; when n = 2, b = 4; when n = 3, b = 6.
From this pattern, we can form the expression as:
b = 2n
So, for a 20 step staircase, you can substitute n = 20 into the expression:
b = 2 * 20
b = 40
Hence, you would need 40 blocks for a 20-step staircase.
I hope that helps! Let me know if you have any more questions.