What is the 6th term of the geometric sequence where a1 1024 and a4 -16?

In a geometric sequence, the nth term can be expressed as ( a_n = a_1 \cdot r^{(n-1)} ), where ( a_1 ) is the first term and ( r ) is the common ratio. Given ( a_1 = 1024 ) and ( a_4 = -16 ), we can set up the equation ( -16 = 1024 \cdot r^3 ) to find ( r ). Solving for ( r ), we get ( r^3 = -\frac{16}{1024} = -\frac{1}{64} ), so ( r = -\frac{1}{4} ). Finally, the 6th term is ( a_6 = 1024 \cdot \left(-\frac{1}{4}\right)^5 = 1024 \cdot -\frac{1}{1024} = -1 ).