Question

Determine whether the sequence converges or diverges. If it converges, give the limit. 48, 8, four divided by three, two divided by nine, ...

Answer 1

48, 8 , 4/3,2/9

note that each term after the first one is calculated by multiplying the previous on by 1/6. The sequence converges

Limit = a1 / (1 -r) = 48 / ( 1- 1/6) = 57.6 or 57 3/5

Answer 2

The sequence is decreasing so it is r<1, therefore it is converging

This is the formula for how to find the sum/limit of the convergence (or how to find a infinite geometric sequence): a1/(1-r)

a1=48

r=8/48=.167

Verifying r:

a1/r=48*.167=8.016=8

a1/r^2=48*.167^2=1.338672=1.34

4/3=1.33

(close enough)

Putting it into equation:

a1/(1-r)=48/(1-.167)=48/.833=57.62304922

Answer Choices:

A. Converges; 288/5

B. Converges; 0

C. Diverges

D. Converges; -12432

288/5=57.6

ANSWER IS A. Converges; 288/5