For the geometric sequence 54, 18, 6, ... determine the formula for the general term and then find t9

Question

Please help I don't know how to deal with all the decimals.

Answer 1

Geometric sequences have common ratios.  As you can see, the terms are decreasing. Therefore, the ratio will be a fraction.

 

If 54/18 is 3 and 18/6 is 3, then just take the reciprocal of this ratio.  The ratio is 1/3.

 

 

Geometric sequence is then

 

t_n = 54(1/3)^{t - 1}

 

 

Plug in t=9 to the to find the 9th term in the sequence.