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.
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
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.
THANKS SO MUCH!!
But im stuck on this question now... only b)
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