Question

A geometric sequence is defined by the recursive formula t1 = 64, tn =

tn - 1 / 2, where n ∈N and n > 1. The sequence is

A) -64, -16, -8, -4, -2, -1, ...
B) 64, 16, 8, 4, 2, 1, ...
C) 64, 32, 16, 8, 4, 2, ...
D) 64, 128, 256, 512, 1024, 2048, ...

Answer 1

C) 64, 32, 16, 8, 4, 2, ...

Explanation:

`t_1=64\\\\t_n=(t_(n-1))/(2)\\\\\text{Therefore}\\\\t_2=(t_1)/(2)\to t_2=(64)/(2)=32\\\\t_3=(t_2)/(2)\to t_3=(32)/(2)=16\\\\t_4=(t_3)/(2)\to t_4=(16)/(2)=8\\\\t_5=(t_4)/(2)\to t_5=(8)/(2)=4\\\\t_6=(t_5)/(2)\to t_6=(4)/(2)=2\\\\t_7=(t_6)/(2)\to t_7=(2)/(2)=1\\\vdots`