The perimeter (distance around the shape) of a rectangle is 40 cm. The length is 14 cm. Let x = width of the rectangle.

Ravi says he can find the width using the equation 2(x + 14) = 40.
Fran says she can find the width using the equation 2x + 28 = 40.

Answer the questions to solve the equations and to compare the steps and solutions.

What is the value of x in Fran's equation, 2x + 28 = 40?

x=6

Step-by-step explanation:

You can take 40-28= 12

So that means 12+28=40

Now since it's taking 2 times x, and we're trying to figure out x, you take 12 divided by 2, and that'll equal 6.

6x2=12

12+28=40

16

step-by-step explanation:

2 x 40 = 80

80/5

= 16

, 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