Enter a recursive rule for the geometric sequence.

2, 6, 18, 54, …

a1=____ ; an=____

The one and the n are both subscript facing down so like an exponent just a lower exponent.

awsometrunt14 Dec 20, 2018

#2**+2 **

a_{1} = 2 = 1st term

We need to find the common ratio from one term to the next

r = common ratio = subsequent term / previous term = 6/2 = 3

To find any term, a_{n}.....we have

a_{n} = a1 * r^{(n - 1)} = 2(3)r^{n-1} where n is the nth term

So....for example....if we wanted the 4th term...we have

2 (3)^{ 4-1} = 2(3)^{3} = 2*27 = __ 54__ .....as expected !!!

CPhill Dec 20, 2018