Question

Fill in the table to help you make a conjecture about the geometric sequence An=(0.5)n-1

N=1,2,3,4,5
A1=1,0.5,0.25,W,0.0625
Sn=1,1.5,x,y,1.9375

W=? X=? Y=?

Answer 1

The next answers are approaching a number and 2

Explanation:

Answer 2

W = 0.125

X = 1.75

Y = 1.875

Explanation:

The geometric sequence looks like of first term 1 , and of common ratio (r=0.5).

Therefore each new term is found by multiplying the previous one by 0.5:

A1 = 1

A2 = 0.5

A3 = 0.25

A4 = 0.125 = W

A5 = 0.0625

And the partial sums are the additions of the terms until the last one considered:

S1 = 1

S2 = 1.5

S3 = 1.75 = X

S4 = 1.875 = Y

S5 = 1.9375

therefore,

W = 0.125

X = 1.75

Y = 1.875