This is a geometric progression, where the terms in the series are.
a, ar, ar^2, ar^3, ar^4, ar^5, ... the first six terms of the series.
Sum of third and fourth terms = s1 = ar^2 + ar^3
s1 = ar^2(1+r) = 3
Sum of fifth and sixth terms = s2 = ar^4 + ar^5
s2 = ar^4(1+r) = 27
dividing s1 by s2,
1/r^2 = 1/9
r = 3
Substituting for r = 3 into s1,
a(3)^2(1+3) = 3
a*36 = 3
a = 1/12
The first term is: a = 1/12