In finding the nth term of a geometric progression you'll have the formula:
[tex]a_n = a_! r^{n-1} [/tex]
where an is the nth term
a1 is the first term
n is the number of terms
r is the common ratio
for that particular problem, you have the given as:
an (a5) = 12
a1 = 3
n = 5
finding r you'll have:
[tex]a_6 = a_1 r^{5-1} [/tex]
[tex]12 = 3 r^4[/tex]
[tex]r^4 = 4[/tex]
[tex]r = \sqrt{2} [/tex]
getting the 2nd, 3rd and 4th terms you'll have:
[tex]a_2 = 3( \sqrt{2}) [/tex]
[tex]a_2 = 3 \sqrt{2} [/tex]
[tex]a_3 = 3 \sqrt{2} ( \sqrt{2}) [/tex]
[tex]a_3 = 6[/tex]
[tex]a_4 = 6 ( \sqrt{2}) [/tex]
[tex]a_4 = 6 \sqrt{2} [/tex]
therefore you'll have the geometric series as:
3, 3√2, 6, 6√2, 12
