`a_1 = 5, a_(k + 1) = -2a_k` Write the first five terms of the geometric sequence. Determine the common ratio and write the nth term of the...

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 = -2`

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

`a_2 = a_1*q => a_2 = 5*(-2) => a_2 = -10`

`a_3 = a_2*q => a_3 = -10*(-2) => a_3 = 20`

`a_4 = a_3*q => a_4 = 20*(-2) => a_4 =-40`

`a_5 = a_4*q => a_5 = -40*(-2) => a_5 = 80`

Hence, evaluating the five terms of geometric sequence yields `a_1 = 5,  a_2 = -10, a_3 = 20, a_4 = -40, a_5 = 80.`