SOLUTION: A geometric sequence has all positive terms. The sum of the first two terms is 15 and the sum of infinity is 27. Find the value of (a) The common ratio; (b) The first term;

Algebra.Com
Question 392679: A geometric sequence has all positive terms. The sum of the first two terms is 15 and the sum of infinity is 27. Find the value of
(a) The common ratio;
(b) The first term;
Thank you :)

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi
sum of the first two terms is 15 for a geometric series
, where r is the common ratio






27 = 15/(1-r^2)
1-r^2 = 15/27
r^2 = 12/27 = 4/9
r = 2/3 sequence has all positive terms..tossing out negative solution for r
(b) The first term;




RELATED QUESTIONS

The sum of the first two terms of a geometric sequence is 90. The sum of the sixth and... (answered by htmentor)
The sum to infinity of a geometric sequence is 27/2 while the sum of the first three... (answered by ikleyn)
First question: A geometric sequence consisting of four terms in which ratio is... (answered by robertb)
the sum of the first two terms of a geometric series is 1 and the sum of its first four... (answered by josgarithmetic)
I can't seem to figure out how to start with this problem... The sum of the first two... (answered by rothauserc)
The seventh term of a geometric sequence is twice the fifth term and the sum of the first (answered by ikleyn)
find a geometric progression of four terms in which the sum of the first and last terms... (answered by josgarithmetic)
the sum to infinity of a geometric progression is twice the sum of the first two terms.... (answered by stanbon,ramkikk66)
An arithmetic sequence of 15 terms has a sum of 3060. The common difference and each... (answered by greenestamps)