# 2 questions on geometric sequences

• Mar 17th 2013, 01:22 PM
M670
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
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
• Mar 17th 2013, 01:54 PM
Shakarri
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 a1
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.
• Mar 17th 2013, 02:19 PM
M670
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?
• Mar 17th 2013, 03:09 PM
HallsofIvy
Re: 2 questions on geometric sequences
Quote:

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.

Quote:

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?
• Mar 17th 2013, 03:34 PM
M670
Re: 2 questions on geometric sequences
Quote:

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.?