2 questions on geometric sequences

For each sequence, find a formula for the general term, http://webwork.mathstat.concordia.ca...4d6db40f51.png. For example, answer http://webwork.mathstat.concordia.ca...ee1469ece1.png if given the sequence:

http://webwork.mathstat.concordia.ca...fd368eabc1.png

**1.** http://webwork.mathstat.concordia.ca...f8af3fc631.png really to sure about this one

**2.** http://webwork.mathstat.concordia.ca...56bff02c41.png 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 http://webwork.mathstat.concordia.ca...c2a19bc431.png

its fifth partial sum http://webwork.mathstat.concordia.ca...bcbb006481.png .

its http://webwork.mathstat.concordia.ca...70877535c1.pngth partial sum http://webwork.mathstat.concordia.ca...4b2ec862c1.png .

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

Re: 2 questions on geometric sequences

1. This isn't a geometric sequence. You can factorise out 1/2 so that it becomes

$\displaystyle \frac{1}{2} (\frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, ... )$

2. This one is a geometric sequence.

The general form for a geometric sequence is $\displaystyle a_n = ar^{n-1}$

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 a_{1}

Find the common ratio which is $\displaystyle \frac{a_{n+1}}{a_n}$ for all values of n

The fifth partial sum is $\displaystyle a_1+a_2+a_3+a_4+a_5$

Likewise, the nth partial sum is $\displaystyle a_1+a_2+a_3+...+a_n$

The sum of the first n terms is equal to $\displaystyle a\frac{1-r^n}{1-r}$

To find the fifth partial sum you could find the first 5 terms and add them up, or use that formula.

Re: 2 questions on geometric sequences

So then for #1 a_{n}=1(1/2)^{(n-1)} and #2 a_{n}=(1/2)(1/2)^{(n-1)}

Now for the second question a_{1}=3/3^{1} does this make sense or am I way off?

Re: 2 questions on geometric sequences

Quote:

Originally Posted by

**M670** So then for #1 a_{n}=1(1/2)^{(n-1)} and #2 a_{n}=(1/2)(1/2)^{(n-1)}

which is equal to 1/2^{n}.

Quote:

Now for the second question a_{1}=3/3^{1} does this make sense or am I way off?

Yes, the first term of (3/3^{n}) is 3/3= 1. Now can you answer the last two questions?

Re: 2 questions on geometric sequences

Quote:

Originally Posted by

**HallsofIvy** which is equal to 1/2^{n}.

Yes, the first term of (3/3^{n}) 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 S_{5}=1.4814 or is it .01234567

Then S_{n}=not sure.?