Asked by Risper
                in a geometric progression, the first term is a and the common ratio is r. the sum  of the first two terms is 12 and the third term is 16.
a) determine the ratio (ar^2)/a+ar( aready found the answer as 4/3)
b) if the first term is larger than the second term, find the value of r.
            
        a) determine the ratio (ar^2)/a+ar( aready found the answer as 4/3)
b) if the first term is larger than the second term, find the value of r.
Answers
                    Answered by
            mathhelper
            
    a + ar = 12
ar^2 = 16
ar^2/(a(1 + r)) = 16/12
r^2/(1+r) = 4/3 <==== you had that
3r^2 = 4 + 4r
3r^2 - 4r - 4 = 0
(r-2)(3r+2) = 0
r = 2 or r = -2/3
if r = 2,
ar^2 = 16 , a = 4 , and the sequence is 4, 8, 16, ...
if r = -2/3,
a(4/9) = 16, a = 36, and the sequence is 36, -24, 16,
but it said, term1 > term2, so it must be the 2nd sequence, where
r = -2/3
    
ar^2 = 16
ar^2/(a(1 + r)) = 16/12
r^2/(1+r) = 4/3 <==== you had that
3r^2 = 4 + 4r
3r^2 - 4r - 4 = 0
(r-2)(3r+2) = 0
r = 2 or r = -2/3
if r = 2,
ar^2 = 16 , a = 4 , and the sequence is 4, 8, 16, ...
if r = -2/3,
a(4/9) = 16, a = 36, and the sequence is 36, -24, 16,
but it said, term1 > term2, so it must be the 2nd sequence, where
r = -2/3
                    Answered by
            Orji esther
            
    No idea
    
                    Answered by
            Juma 
            
    Sum of 2nd term and 3rd term is 12 and sum of 4th term and 5th term is 300 in g.p .find first term and common ratio 
    
                                                    There are no AI answers yet. The ability to request AI answers is coming soon!
                                            
                Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.