Question 1167353: In this problem, you are stacking bricks. Every row contains one more brick than the row above it. The instructions say to determine a quadratic function to model the total number of bricks in the stack,f(x), given a number of rows, x. However, I'm unable to create a function that makes sense for this problem. I'm aware that the pattern is that every time a row is created it has 1 more brick than the previous (the one of above it) row. I need help creating the quadratic function.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The only way this problem makes sense is if the top row contains 1 brick.
Otherwise, there is no way to know how many bricks we are starting with
on the top row.
The number of bricks in the x-th row, can be represented by an arithmetic sequence: a_x = a_1 + (x-1)*d,
where d = the common difference = 1,
and a_1 = the first term = 1
The sum of the first x terms of an arithmetic sequence is:
S_x = (x/2)(a_1 + a_x) = (x/2)(1 + a_x)
But a_x = 1 + (x - 1) = x
Thus S_x = f(x) = (x/2)(1 + x) = x^2/2 + x/2
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