Question

a grocery 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?

Answer 1

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!