SOLUTION: The sum of the first two terms of a geometric series is 90. The third term is 24. A. Show That there are two possible series and find the term and the common ration in each case

Question 1092202: The sum of the first two terms of a geometric series is 90. The third term is 24.
A. Show That there are two possible series and find the term and the common ration in each case.
B. Show that both series converge and find their respective sums.
Answer by greenestamps(13330) (Show Source): You can put this solution on YOUR website!

The third term is 24:

--> (1)

The sum of the first two terms is 90:

(2)

Substitute (1) into (2):

The two values of the common ratio are -2/5 and 2/3.

For the common ratio -2/5, the first term a is

That gives us the sequence 150, -60, 24, ...

For the common ratio 2/3, the first term a is

That gives us the sequence 54, 36, 24, ...

RELATED QUESTIONS
the sum of the arithmetic serie whose first two terms are -12 and -8, respectively, and... (answered by mananth,MathLover1)

the sum of the first two terms of a geometric series is 1 and the sum of its first four... (answered by josgarithmetic)

The sum of the first three terms of a geometric series is 14 and the product of the first (answered by richard1234)

The second term in a geometric series is 36. The sum of the first two terms is -18. What... (answered by Edwin McCravy)

the first and second terms of a geometric sequence is 108 and the sum of the third and... (answered by josgarithmetic)

sum of a geometric series is 46.5. The first term of the series is 24, and its common... (answered by jim_thompson5910,MathTherapy)

The first two terms of a geometric sequence and an arithmetic sequence are the same. The... (answered by Edwin McCravy)

The sum of the second and third terms of a geometric progression is six times the fourth... (answered by ikleyn)

The third term of a geometric progression is nine times the first term. The sum of the... (answered by ikleyn)