geometric sequences

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May 1st 2008, 04:59 PM
Airjunkie

geometric sequences

Given the following geometric sequence: 32, ____, ____,4,.........

Find the missing two terms

find the nth term

find the sum of the first 5 terms

find the sum of all the terms. Explain your answer
May 1st 2008, 05:12 PM
Mathstud28

Quote:

Originally Posted by Airjunkie

Given the following geometric sequence: 32, ____, ____,4,.........

Find the missing two terms

find the nth term

find the sum of the first 5 terms

find the sum of all the terms. Explain your answer

Examine $a_n=32\bigg(\frac{1}{2}\bigg)^{n}$
May 1st 2008, 05:15 PM
Airjunkie

so i solve that by plugging in 2, 3, and 5 in for n? That would give me the first 5 numbers.
May 1st 2008, 05:18 PM
Mathstud28

Quote:

Originally Posted by Airjunkie

so i solve that by plugging in 2, 3, and 5 in for n? That would give me the first 5 numbers.

Yes...the corresponding natrual number you put in will yield the n-th term
May 1st 2008, 05:21 PM
Airjunkie

I have no idea what im doing.
May 1st 2008, 05:26 PM
Mathstud28

Quote:

Originally Posted by Airjunkie

I have no idea what im doing.

Explain what you would do? Give me any inkling you have?
May 1st 2008, 05:37 PM
Airjunkie

I dont know,

I thought i could do

Gn = G1 * r^n-1

I need some help bad.
May 1st 2008, 05:42 PM
Mathstud28

Quote:

Originally Posted by Airjunkie

I dont know,

I thought i could do

Gn = G1 * r^n-1

I need some help bad.

Do you agree that this is the correct sequence? and yes that is the value for the sum of a geometric series
May 1st 2008, 08:49 PM
Airjunkie

No answers eh? Well shoot, if anyone can help me ill try to check this later tonight, maybe i can sneak into the library b4 math.

Thanks,

Airjunkie
May 1st 2008, 11:03 PM
Daddycakes

Quote:

Originally Posted by Airjunkie

Given the following geometric sequence: 32, ____, ____,4,.........

Find the missing two terms

find the nth term

find the sum of the first 5 terms

find the sum of all the terms. Explain your answer

Ok based on the given we can observe that the sequence is decreasing by n(1/2). That gives us the complete sequence: 32,16,8,4.
There is a formula for this but it requires two consecutive numbers in a series which is rn=an / an-1

the nth term can be calculated by the formula an=a1r^n-1. We already determined that r=1/2 above. So we just need to plug in our values
an=32* (1/2)^n-1. We can now use this formula to calculate any of the n terms we would like.

Sum of the first 5 terms is done by the formula: Sn=a1 (1-r^n)/1-r
So we plug in our Values:
S5=32(1-1/2^5)/1-1/2 >> S5=32(1-1/32)/.5 >> S5=32(31/32)/.5 S5 = 62

For the last part we use the formula: Sinfinity= a1 /1-r
this formula has a condition though the conditions are "r" must be between -1 & 1 for it to have an infinite series. Since our "r" value was 1/2 we are able to use this.

Sinfinity= 32/1-.5 = 32/.5 = 64

Hope this helps