sequence problem

[nellyp]

i have a problem i need to solve. It is the sequence 7, -7, 14, -42, 168,... they require the next 3 numbers. I have tried this, and though I can answer simpler questions this is beyond me. Any help would be appreciated. Is there a formula i can follow to help me with this, as I have answered all the other questions and am worried this type will crop up again.

 

[pka]

i have a problem i need to solve. It is the sequence 7, -7, 14, -42, 168,... they require the next 3 numbers.

First, I hate this type question because the is no one correct answer.

However, this answer works.
Let \(\displaystyle a_0=7\) then if \(\displaystyle n\ge 1\) define \(\displaystyle a_n=(-1)^{n}n\cdot |a_{n-1}|\).

 

[soroban]

Hello, nellyp!

\(\displaystyle \text{Find the next three numbers: }\:7,\;-7,\;14,\;-42,\;168\;\hdots\)

Note what happens from term to term . . .

. . \(\displaystyle \begin{array}{c|cccccccccc}\text{Sequence} & 7 && \text{-}7 && 14 && \text{-}42 && 168 \\ \hline \text{Operation} && \times(\text{-}1) && \times(\text{-}2) && \times(\text{-}3) && \times(\text{-}4) \end{array}\)


Get it?

 

[lookagain]

i have a problem i need to solve.
It is the sequence 7, -7, 14, -42, 168,...
they require the next 3 numbers.

As pka (and certain others) have stated, there is no one correct
answer in these types of sequence problems (as it is what the
problem poser has in mind). This is true unless it is stated what
kind of sequence it is.


Anyway, you can write the sequence as:


\(\displaystyle 7(1, -1, 2, -6, 24, ...) \ = \)


\(\displaystyle 7(0!, -1!, 2!, -3!, 4!, ...)\)


So, an explicit formula would be:


\(\displaystyle 7(n - 1)!(-1)^{n - 1}\)

 

[tkhunny]

Someone needs to say it. The next three numbers are -2, -2, and -2. :lol:

Anything you can explain should be accepted as a correct response.