SOLUTION: The sum of the first two terms of a geometric progression is 5/2,and the sum of the first four teems is 65/18,find the third term of the G.P if r is greater than 0
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-> SOLUTION: The sum of the first two terms of a geometric progression is 5/2,and the sum of the first four teems is 65/18,find the third term of the G.P if r is greater than 0
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Question 1112262: The sum of the first two terms of a geometric progression is 5/2,and the sum of the first four teems is 65/18,find the third term of the G.P if r is greater than 0 Answer by greenestamps(13203) (Show Source):
The sum of the first two terms is 5/2, and the sum of the first four terms is 65/18. So the sum of the 3rd and 4th terms is .
The third term is the first term multiplied by the common ratio r twice; the fourth term is the second term multiplied by r twice. So the sum of the third and fourth terms is the sum of the first two terms, multiplied by the common ratio twice: because the problem says r is positive
The fourth term is the third term multiplied by r=2/3; so the sum of the third and fourth terms is the third term plus 2/3 of the third term:
Answer: The third term of the sequence is 2/3.
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Having posted that solution, I see there is what I think is a slightly easier way to find the common ratio....
Since the third term is the first term multiplied by the common ratio r twice and the fourth term is the second term multiplied by r twice, the sum of the first four terms is the sum of the first two terms, plus the sum of the first two terms multiplied by r twice:
Then from there proceed as in the earlier solution I showed.
