# Find the nth-term of the sequence whose first few terms are written out?

##### 2 Answers

#### Explanation:

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.

Take,

#### Explanation:

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 :