Marissa has determined that there is a relationship between the scale factor and perimeter of an image and its pre-image and between the scale factor and area of an image and its pre-image.
(a) For both the picture and the mat, determine the ratios of the perimeter of the scaled image to the
4.
perimeter of the original item.
(c) For both the picture and the mat, determine the ratios of the area of the scaled image to the area of
the original item.

, 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

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step-by-step explanation: