Question

Find the sum of the geometric sequence. 1, one divided by two, one divided by four, one divided by eight, one divided by sixteen

Answer 1

The equation for a finite geometric sequence is Sn=a1((1-r^n)/(1-r))

a1=1

r=.5/1=.5

n=5

Using the equation:

Sn=a1((1-r^n)/(1-r))=1((1-.5^5)/(1-.5))=1((1-.03125)/(1-.5))=1(.96875/.5)=1*1.9375=1.9375

Answer Choices:

A. 1/12 or .083

B. 93

C. -1/48 or -.02083

D. 31/16 or 1.9375

The Answer is D. 31/16

Answer 2

$a_1=1;\ a_2=\dfrac{1}{2};\ a_3=\dfrac{1}{4};\ a_4=\dfrac{1}{8};\ a_5=\dfrac{1}{16};\ ...\\\\d=a_2:a_1\\\\d=\dfrac{1}{2}:1=\dfrac{1}{2}\\\\|d| \ \textless \ 1\ therefore\ the\ sum\ S\ of\ the\ geometric\ sequence\ is\ equal:\\\\S=\dfrac{a_1}{1-q}\\\\subtitute\\\\S=\dfrac{1}{1-\frac{1}{2}}=\dfrac{1}{\frac{1}{2}}=1\cdot\dfrac{2}{1}=2\\\\\\Answer:\boxed{S=2}$