GEOMETRIC SEQUENCES

Question

1 Determine if the following sequence is geometric. If yes, state the value of r: 20, 40, 80, 160,...

Select one:

a. No, it is not a geometric sequence.

b. Yes, the value of r is 20

c. Yes, the value of r is 2

d. None of the above

2 Find three geometric means between 10 and 2,560.

What is the value of r?

Select one:

a. 2

b. -2

c. 4

d. ±4

 

 

 

Answer 1

1)

The sequence is 20, 40, 80, 160,..

Geometric sequence is a sequence with a constant ratio between successive terms.

Find the common ratio:

r = t2/t1 = t3/t2=............. = tn/tn-1

r = 40/20 = 80/40 = 160/80 = 2

So sequence is geometric sequence with r = 2

Option c is correct.

Answer 2

10, - , - , - , 2560

so that the three terms will be a geometric sequence.

We use the formula

tn = ar^(n-1)

First term a = 10

t5 = ar^(5-1)

2560 = 10r^4

r^4 = 256

r^4 = 4^4

r =4

Option C is correct

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Find the three geometric means.

t2 =ar

    = (10)(4)

     =40

t3 =ar ^2

    = (10)(4)^2

     = 160

t4 =ar^3

    = (10)(4)^3

     = 640

So the geometric means are  40,160 , and  640