# Thread: 2 questions on geometric sequences

1. ## 2 questions on geometric sequences

For each sequence, find a formula for the general term, . For example, answer if given the sequence:

2. in this one I see the pattern that 1/4 is half of 1/2 and 1/8 is half of 1/4 and 1/16 is half of 1/18 but I just can't seem to figure out the formula to show this

And the next question is
For the sequence
its fifth partial sum .
its th partial sum .

Any explanation into what exactly is being asked would be great I went back to my chapter twice and still can't figure out the partial sum part of sequeneces
Thanks Guys

2. ## Re: 2 questions on geometric sequences

1. This isn't a geometric sequence. You can factorise out 1/2 so that it becomes
$\frac{1}{2} (\frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, ... )$

2. This one is a geometric sequence.

The general form for a geometric sequence is $a_n = ar^{n-1}$
Where a is the first term and r is the common ratio

Each term is half of the previous so the common ratio is 1/2, and the first term is 1/2.

3. Find the first term a1
Find the common ratio which is $\frac{a_{n+1}}{a_n}$ for all values of n

The fifth partial sum is $a_1+a_2+a_3+a_4+a_5$
Likewise, the nth partial sum is $a_1+a_2+a_3+...+a_n$

The sum of the first n terms is equal to $a\frac{1-r^n}{1-r}$
To find the fifth partial sum you could find the first 5 terms and add them up, or use that formula.

3. ## Re: 2 questions on geometric sequences

So then for #1 an=1(1/2)(n-1) and #2 an=(1/2)(1/2)(n-1)
Now for the second question a1=3/31 does this make sense or am I way off?

4. ## Re: 2 questions on geometric sequences

Originally Posted by M670
So then for #1 an=1(1/2)(n-1) and #2 an=(1/2)(1/2)(n-1)
which is equal to 1/2n.

Now for the second question a1=3/31 does this make sense or am I way off?
Yes, the first term of (3/3n) is 3/3= 1. Now can you answer the last two questions?

5. ## Re: 2 questions on geometric sequences

Originally Posted by HallsofIvy
which is equal to 1/2n.

Yes, the first term of (3/3n) is 3/3= 1. Now can you answer the last two questions?
The first two I am confused with (1/2)^n
And the second part I have S5=1.4814 or is it .01234567
Then Sn=not sure.?