`a_1 = 81, a_(k + 1) = (1/3)a_k` Write the first five terms of the geometric sequence. Determine the common ratio and write the nth term of...

You need to write the 5 terms of the geometric sequence, hence, since the problem provides the first term, you need the ratio q. You may evaluate the ratio using the relation:

`a_(k+1) = a_k*q`

`q = (a_(k+1))/(a_k) => q = 1/3`

You may evaluate `a_2, a_3, a_4, a_5` , such that:

`a_2 = a_1*q => a_2 =81*(1/3) => a_2 = 27`

`a_3 = a_2*q => a_3 = 27*(1/3) => a_3 = 9`

`a_4 = a_3*q => a_4 = 9*(1/3) => a_4 =3`

`a_5 = a_4*q => a_5 = 3*(1/3) => a_5 = 1`

Hence, evaluating the five terms of geometric sequence yields `a_1 =81, a_2 = 27, a_3 = 9, a_4 = 3, a_5 = 1.`