The sequence is:
If we look at the numerator (top) of the fractions only, we can see that the function will give us an alternating
That gives us our alternating signs in the sequence, starting with negative, and it also provides us with a
If we look at the denominator (bottom) of the fraction only, we can see that the function will give us
To check, you can calculate the fifth number in the sequence from the formula:
Take a look at the sequence and see what is changing from term to term. Pick the sequence that matches these guidelines.
The correct answer is B.
We observe these conditions in the sequence:
- The first term is
#–1#(which we can think of as #–1/1#).
- In each new term, the denominator is going up by 3.
- The terms alternate between negative and positive.
The correct formula will be the one that satisfies these conditions.
The correct answer CANNOT be A, since the terms it will generate do not alternate in sign. (Its terms will always be negative for any
The correct answer CANNOT be C, because when
The correct answer CANNOT be D, since when
That means the answer should be B. Looking at the formula in B, we see that the terms it will generate...
- ...begin with
- ...will alternate in sign (thanks to the
#(–1)^n#in the numerator), and
- ...their denominators go up by 3 (because of the coefficient of
#3#on the #n#).
To test this, we try
This is clearly generating the sequence we are trying to match. Thus, B is the answer.