Agrocery clerk is making a display of oranges. the number of oranges in the layers of display form a sequence, with the top layer counting as layer 1. the explicit rule f(n) = (n + 1) squared describes this sequence, where n is a whole number greater than 0. will 50 oranges be enough to complete the top 4 layers of the display?

If there is 1 at the top, then you have 1, then 2, then 3, etc.

total number of oranges equals:

1 + 2 + 3 + ... + 16 + 17 + 18 <-- stop @ 18 because this is the number of oranges at the base

You can use the formula:

sum of first n numbers = n*(n + 1)/2

-->

18*19/2 = 9*19 = 171

or you can figure it out (basically derive the above formula):

you have:

1 + 18 = 19

2 + 17 = 19

3 + 16 = 19

...

How many pairs do you have?  Well, it's just the number of numbers: 1-18 = 18 numbers (divide by 2) = 9 pairs)

9 pairs of 19 = 9 * 19 = 171

Hope this helps!

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.