`a_1 = 6, a_(k + 1) = -(3/2)a_k` Write the first five terms of the geometric sequence. Determine the common ratio and write the nth term of...

You may find the ratio of the geometric sequence, such that:

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

`q = -3/2`

You may write the first 5 terms, such that:

`a_2 = a_1*q => a_2 = 6*(-3/2) => a_2 = -9`

`a_3 = a_2*q => a_3 = 27/2`

`a_4 = a_3*q => a_4 = -81/4`

`a_5 = a_4*q => a_5 = 243/8`

You may write the n-th term such that:

`a_n = a_1*q^(n-1) => a_n = 6*(-3/2)^(n-1)`

Hence, evaluating the first five terms and the n-th term yields a`_1 = 6, a_2 = -9, a_3 = 27/2, a_4 = -81/4,a_5 = 243/8, a_n = 6*(-3/2)^(n-1).`