in a GP, the sum of the 3rd and 4th terms is -4/3 and the sum of the 4th and 5th terms is -4/9. Find the 6th term.

Answer 1

a, ar ar^2 ar^3 ar^4

a r^2 + a r^3 = -4/3
a r^3 + a r^4 = -4/9

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

-4/(3 a r^2) = -4/(9 a r^3)
so
r = 1/3
a(1/9)(4/3) = -4/3
a = -9
so:
-9 -3 -1 -1/3 -1/9 and -1/27

Answer 2

√33π= 5.7445626