Question

What is the 6th term in the geometric sequence where a1= 1,024 and a4= -16?

Answer 1

The answer is -1

$a_n= a_1r^{n-1}$

a₁ - the first term
r - the common ratio
n - the desired term

We have:
a₁ = 1024
a₄ = -16
n = 4
r = ?

$a_4= a_1r^{4-1} \\ -16=1024*r^{3} \\ r^{3} = -16/1024 \\ r^{3} = - 0.015625 \\ r= \sqrt[3]{-0.015625} \\ r = -0.25$

We have:
a₁ = 1024
a₄ = -16
n = 4
r = -0.25
a₆ = ?

$a_6= a_1*r^{6-1} \\ a_6= 1024*(-0.25)^{5} \\ a_6=1025*(-0.00098) \\ \\ a_6= -1$