Question

-- QUESTION FOLLOWS --------------------------

Answer 1

I figured it out but was thrown off by the poor wording used. Please always copy the question exactly how it is given to you otherwise you might not get any help or wrong answer.

terms of geometric sequence
A(n) = ar^(n-1)
where "a" represents first term
here you are given information to set up two equations in two variables "a" and "r". you must combine equations to solve for one variable at a time.

A(4) - A(3) = 9
(ar^3) - ar^2 = 9
a(r^3/2 - r^2) = 9
a = 9/(r^3-r^2)

A(5) - A(4) = 13.5
ar^4 - ar^3 = 13.5
a(r^4 - r^3) = 13.5

combined
9/(r^3 - r^2) * (r^4 - r^3) = 13.5
cross multiply
9r^4 - 9r^3 = 13.5r^3 - 13.5r^2
combine like terms
9r^4 - 22.5r^3 + 13.5r^2 = 0
factor/polysolver
r = 3/2 or r = 1
but r cannot equal 1

ratio is 3/2 = 1.5

a = 9/(1.5^3 - 1.5^2) = 8
first term is 8