The dimensions of a box of paper clips are 3.1 inches by 1.6 inches by 1 inch. If there are 100 paper clips guaranteed to be in each box, what is the approximate density of paper clips per cubic inch?

0.0496 in^3

First, find the volume of the box, in inches:

3.1 * 1.6 * = 4.96

Then, find the density of the 100 paper clips:

(let d = density)

100d = 4.96

d =  0.0496

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for