Question

What is the 7th term of the geometric sequence where a1 = 256 and a3 = 16? a) 0.03125 b) 0.0625 c) 0.125 d) 0.15625

Answer 1

HI,

Answer B: 0.0625

Explanation:

`a_1=256=2^8\\\\a_3=16=2^4\\\\(a_3)/(a_1) =(16)/(256) =(1)/(16)=r^2\\\\r=(1)/(4)=2^(-2) \ or\ r=-(1)/(4)=-2^(-2) \\\\a_7=a_1*r^6=2^8*2^(-2*6)=(1)/(2^4) =(1)/(16) =0.0625\\`