Read the following: “The length of a rectangle is two feet greater than twice its width. If the perimeter is 25 feet, find the width.” Which of the following translations is correct? (Hint: Draw a figure.) 25 = 2L + 2(2 + 2W)
25 = 2(2 + 2W) + 2W
25 = 2L + 2(2 + L)
None of these choices is correct.

, 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

just sum

10 + 10 = 20