A brick staircase has a total of 16 steps.......

O

ochocki

New member
Joined
Feb 7, 2005
Messages
46
A brick staircase has a total of 16 steps, the bottom step requires 103 bricks. Each successive step requires 4 less bricks than the prior one. How many bricks are required to build the staircase?

I know this is some kind of sequence problem, I just don't know how to set it up, can anyone give me a little help please?
 
ochocki said:
I just don't know how to set it up
Click to expand...
Each term of the sequence has a (negative) difference of 4. What sort of sequence is this? What is the (algebraic) form of the n-th term? What is the formula for the sum of the sixteen terms?

Eliz.
 
I feel like I am so close. It's obviously an arithmetic sequence. Here is what I am plugging in, the answer just doesnt make sense.

an=a+(n-1)d

103=a+(16-1)-4

simplified

a=163

Is this correct or did i miss a step?
 
a is the first term in the sequence and an is the n-th term, at least I thought they were. When i plug in my numbers the value I get for a is higher that the 16th term. That seems impossible because d=-4
 
Try this sum: \(\displaystyle \L \sum\limits_{k = 0}^{15} {\left( {103 - 4k} \right)} .\)
 
how can it be 163 bricks in all?
Each step has 4 bricks less than the previous. The first step has 103 bricks.

first step is 103
second step is 99
third step is 95

just those 3 steps = a total of 287 bricks.
 
Man, this just will not click with me. I'm so bad with these, can you guys give me any more examples/advice on this?
 
\(\displaystyle \L\sum\limits_{k = 0}^{15} {\left( {103 - 4k} \right)} = 1168\)
 
ochocki said:
Man, this just will not click with me. I'm so bad with these, can you guys give me any more examples/advice on this?
Click to expand...

Ochocki, pka gave you a summation, which is probably beyond what you have seen in your current math class....

All it means is the sum of all (103-4k) with consecuative k = 0 to 15

so (103-4(0))+(103-4(1)+....

This could be expressed using a recursive formula.
 
jwpaine said:
Ochocki, pka gave you a summation, which is probably beyond what you have seen in your current math class....
Click to expand...
You don’t think that Ochocki has a calculator and knows how to use it?
 
ochocki said:
a is the first term in the sequence and an is the n-th term
Click to expand...
So why did you plug the starting value, 103, in for "a<sub>n</sub>", the n-th term, and then try to "solve" for the starting value, "a", which had been given to you?

Instead, try plugging the starting value into the starting-value variable, and solve for the n-th term expression by simplifying the formula for the n-th term.

Eliz.
 
You must log in or register to reply here.
Top