The second term of a geometric series is 24 and the fifth term is 3.

a. Show that the common ratio of the series is 1/2.

b. Find the first term of the series.

c. Find the sum to infinity of the series.(Nerd)

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- February 28th 2010, 07:26 AMansonboundSequences and series
The second term of a geometric series is 24 and the fifth term is 3.

a. Show that the common ratio of the series is 1/2.

b. Find the first term of the series.

c. Find the sum to infinity of the series.(Nerd) - February 28th 2010, 08:06 AMHallsofIvy
That's pretty straightforward- if you know the definitions. The "nth" term of a geometric series with first term a and common ratio r is . Knowing that the second term is 24 tells you that and knowing that the 5th term is 3 tells you that . That gives you two equations to solve for a and r. In particular, if you divide the second equation by the first,

Once you know r, it is easy to use to find a.

And, once you know both a and r, the "sum to infinity" is just

- February 28th 2010, 08:11 AMmasters
Hi ansonbound,

____, 24, ____, ____, 3

Using , we can verify that the common ratio is 1/2

Working to the left of 24, the first term if found by multiplying 24 by 2. Thus, the first term is 48.

The sum S of an infinite geometric series with -1 < r < 1 is given by:

Since , and since , the sum exists.

- February 28th 2010, 02:39 PMansonbound
THANKS SO MUCH!!

But im stuck on this question now... only b)(Rofl)

http://www.mathhelpforum.com/math-he...rst-terms.html - March 1st 2010, 02:17 AMHallsofIvy
"Find the sum of the first ?? terms of the series."

Something is missing! How many terms? - March 1st 2010, 02:41 AMBacterius