Question

find the next 3 terms in the geometric sequence.

1, 4, 16, 64, ...

a)256, 1024, 4096
b) 86, 108, 130
c) 128, 256, 512
d) 96, 192, 288

Answer 1

$a_1=1;\ a_2=4;\ a_3=16;\ a_4=64;\ a_5=?;\ a_6=?;\ a_7=?\\\\r=a_2:a_1\\\\r=4:1=4\\\\a_n=a_1r^{n-1}\\\\a_n=1\cdot4^{n-1}=4^{n-1}\\\\a_5=4^{5-1}=4^4=256\\\\a_6=4^{6-1}=4^5=1024\\\\a_7=4^{7-1}=4^6=4096\\\\Answer:\boxed{256;\ 1024;\ 4096}\to\fbox{a)}$