Staircases

Slot Machine Quiz

You have to walk up each step to get to the top of the staircase.
—Old Turkish Proverb

Drag & Drop Blocks
Click where you want a new Square.
Then Click the Spacebar.

The mathlet above illustrates staircases with one step, two steps, and three steps.
How many blocks are needed to build a staircase with 10, 50, 100, or any number of steps?
Fill in the table and boxes below.
Then show your general formula is true for all positive integers n.
Call your general formula t = f(n).

For 5 points, complete the blue rows in the table below.

Fill in the 3 red boxes above for 1 point each.

Box 1: Formula for the General Term t = f(n)
Use your inductive ability to find the formula for the general term.
The formula will let you know when you find it.

Box 2: What do you Add to each term to get the Next Term?
Enter your expression in the add(n) box.
If it is not a constant, write what you add as an expression of n?
Careful. Is it this n, the last n, or the next n?

Box 3: Formula for Next Term as an expression of n+1
After you have found t = f(n), everywhere you put n, substitute n+1.
Careful. Dont forget the ( ) where they are needed.
Call this formula tnext = f(n+1)

For 2 points, use a little algebra to show that Box 1 + Box 2 = Box 3.
If Box 1 + Box 2 does not equal Box 3, rethink your Algebra and/or your Boxes.

Remember the Order of Operations:

SYMBOL MEANING EXAMPLE RESULT

+ ADD 2+(2+1) = 2+3 = 5

- SUBTRACT 5-(3+1) = 5-4 = 1

* MULTIPLY 4*(7+3) = 4*10 = 40

/ DIVIDE 6/3-2 = 2-2 = 0

^ EXPONENT 3^4 = 3*3*3*3 = 81

( ) PARENTHESES 2*(5-3) = 2*2 = 4