Question

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.

Answer 1

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

Answer 2

No idea

Answer 3

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