Which one of the following is a geometric sequence?

a.2,-3,9/2,-18/4
b.-7,10,23,36
c.0,1,2,3
d.8,4,2,1,1/2,1/4

Explanation:

Each term of sequence D has us multiply by 1/2, or divide by 2, to get the next term.

8 * (1/2) = 4

4 * (1/2) = 2

2 * (1/2) = 1

1 * (1/2) = 1/2

(1/2) * (1/2) = 1/4

and so on

We can divide any term, except the first term, by its prior term to get the common ratio, so for instance,

common ratio = (term2)/(term1) = 4/8 = 1/2

and if we apply this to all possible pairs of consecutive terms then we see that we get 1/2 across the board. This confirms we have a geometric sequence.

The other sequences do not fit this pattern.

For example, choice B has

(term2)/(term1) = 10/(-7) = -1.43

and

(term3)/(term2) = 23/10 = 2.30

those results are not the same; therefore, sequence B is not geometric. The other answer choices can be ruled out in a similar fasion.

whatever you can spend with $11.53 or under.

step-by-step explanation:

20 - 8.47 = 11.53. take away the money he used for lunch from the starting amount of 20.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.