Question

1. Find the common ratio and the 7th term of the sequence 2/9, 2/3, 2, 6, 18, .....

2. The 3rd and 5th terms of a geometric sequence are 2 and 1/2 respectively. What is the first term?

3. Find the geometric mean between:
a. 1/2 and 1/3
b. sqrt5 - sqrt2

Answer 1

common ratio = r = 6/2 = 3 (I took the easiest fraction)

first term = a = 2/9
term7 = ar^6 = (2/9)(3^6) = 162

2. ar^2 = 2
ar^4 = 1/2
divide the 2nd equation by the first
r^2 = 1/4
r = ± 1/2
then in ar^2 = 2
a(1/4) = 2
a = 8

3. a)
x/(1/2) = (1/3)/x
x^2 = 1/6
x = ± 1/√6

b) check your typing
is it √5 and -√2 ?

Answer 2

9