Hector says that the expression will always have the opposite sign as p for all values of p (positive, negative, and 0). Is he correct? Why or why not?
1.No, will always have the opposite sign as p except when p = 0.

2. Yes, ” will always have the opposite sign as p because if p is positive is negative, and if p is negative. ” is positive.

3.No, will always have the same sign as p.

4.Yes, will always have the opposite sign as p because p is positive and when divided by a negative number, the result is negative.

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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