Write an explicit rule and recursive rule for a geometric sequence with a second term of 6 and a third term of 12.

Step-by-step answer:

Given:

Geometric sequence with

second term, T2 = 6

third term, T3 = 12

Wants to have the explicit and recursive rules.

Solution:

common ratio, r = 12/6 = 2

Therefore the first term, T1

= second term / r

= 6/2

=3

Thus the absolute rule is

Tn = T1 * r^ (n-1) where T1 = 3, r=2. Check: T3 = T1*2^ (3-1) = 3*2^2=12 ... good

The recursive rule (depending on the previous term)

Tn = Tn-1*r = 2*Tn-1