Find the nth-term of the sequence whose first few terms are written out?
Okay, so first we have to figure out if this is an arithmetic or geometric sequence.
For an arithmetic sequence, you should have the ability to add a common difference
Then simplify. Remember the double negative turns into a positive. You will then get,
Now we have to check if this difference is applicable to the entire set. I will try to add
That is different than the third term, so we now know that we have a geometric sequence.
The process is similar, but now you want to find the common ratio,
We know this is correct by process of elimination but if you want to check, then take one term multiply it by the common ratio, to see if you get the next term.
Moving onward, we can now create the formula to find the
The basic form for a geometric sequence is
Although, that is assuming that
But, with what we have, we can put in our known information,
Where z is the term number.
The given sequence is :
We can separate the given sequence in two parts.
So, the nth term
where, first term
Hence, for the given sequence,nth term :