There are three consecutive odd integers where the product of the first and second integers is 1 less than 4 times the third. Part A: Which equation represents the verbal description, where n represents the smallest integer?

Part B: What is the factored form of the equation?

Select two answers: one for Part A and one for Part B.

A: n(n+1)=4(n+2)−1
B: This equation cannot be easily written in factored form.
B: (n+1)(n−3)=0
A: n(n+2)=(4n+4)−1
B: (n+3)(n−5)=0
A: n(n+2)=4(n+4)−1

hiking down a winding trail.

step-by-step explanation:

, 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