Question

In a g.p the sum of the 3rd and the 4th terms is -4/3 and the sum of the 4th and the 5th term is -4/9. Determine (A) the first term (B) the common ratio

Answer 1

ar^2 + ar^3 = -4/3 -----> ar^2(1+r) = -4/3
ar^3 + ar^4 = -4/9 ------> ar^3(1+r) = -4/9

divide the 2nd by the first:
r = 1/3

sub it back
a(1/9)(1 + 1/3) = -4/3
a(4/27) = -4/3
a = -9

check:
your GP is
-9, -3,-1, -1/3, -1/9, -1/27, ...
3rd+4th = - 1 - 1/3 = -4/3
4th+5th = -1/3 - 1/9 = -4/9
all is good