Find the measure of each equalateral triangle if AB=2x ,BC=x+7 ,CA=4x-14

X = 7

AB = 14

BC = 14

CA = 14

Step-by-step explanation:

This is an equilateral triangle so you can set the lengths equal to each other in order to find X.

2x=x+7

 -x    -x

x=7

you can do this with any combination of the lengths and you will always get 7

Now you plug in 7 for x

Original: 2x

Plug in 7: 2*7

You get 14

Since this is after all, an equilateral triangle all lengths are equal so all lengths are 14.

, 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