Question

Which represent geometric sequences? A marathon runner runs half of a race, then runs half the distance left to the finish line, then runs half the distance that still remains, and so on. The first movie rental costs $2, and each additional rental costs $1. 10, 1, 0.1, 0.01, … –4, 20, –100, 500, … –1, 5, 11, 17, 23, …

Answer 1

I agree with person above

Explanation:

Answer 2

Explanation:

1). Let the length of a marathon race = x miles

Marathon runner runs this race in the sequence formed as,

`(x)/(2),(x)/(4),(x)/(8).........`

Common ratio =
`((x)/(4))/((x)/(2))`

=
`(x)/(4)* (2)/(x)`

=
`(1)/(2)`

Therefore, it's a geometric sequence.

2). First movie rental cost = $2

Followed by each additional movie rental cost = $1

Therefore, rental of movies will be in the form of a linear equation,

y = 2x + 1

where x = number of movies

And y = Rental of movies

It's not a geometric sequence.

3). 10, 1, 0.1, 0.01.......

Ratio in 2nd and 1st term =
`(1)/(10)=0.1`

Ratio in 3rd and 2nd term =
`(0.1)/(1)=0.1`

Therefore, ratio in each term is common.

Sequence formed will be a geometric sequence.

4).
`\sum_(k=1)^(7)4(0.2)^(k-1)`

Expression represents a common ratio of 0.2,

Therefore, expression given will represent a geometric sequence.

5). -4, 20, -100, 500, ...........

Ratio of 2nd and 1st term =
`(20)/(-4)` = -5

Ratio of 3rd and 2nd term =
`(-100)/(20)`

= -5

There is a common ratio = -5

Therefore, it's a geometric sequence.

6). -1, 5, 11, 17.........

Ratio of 2nd and 1st term =
`(5)/(-1)=-5`

Ratio of 3rd and 2nd term =
`(11)/(5)=2.2`

-5 ≠ 2.2

Therefore, sequence is not a geometric sequence.

7). -500, 100, -20, 4........

Ratio of 2nd and 1st term =
`(100)/(-500)=-(1)/(5)`

Ratio of 3rd and 2nd term =
`(-20)/(100)=-(1)/(5)`