Question

What is the 6th term of the geometric sequence where a1 = −4,096 and a4 = 64?

Answer 1

$a_1=4.096;\ a_4=64\\\\a_4:a_1=r^3\\\\r^3=64:4.096\\\\r^3=15.625\\\\r=\sqrt[3]{15.625}\\\\r=2.5\\\\a_6=a_4r^2\to a_6=64\cdot2.5^2=64\cdot6.25=400\\\\Answer:\boxed{a_6=400}$