Francine was working with a problem involving triangles and parallel lines. She was given the following diagram with AB = 4, BC = 8, and BD=5. She was asked to solve for the length of CE. (a) Francine incorrectly solves for CE as follows:

4/8 = 5/CE -> 4CE = 40 -> CE = 10

Explain why Francine is incorrect in using the Side Splitter Theorem here.​

, 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