Question

SOMEONE PLEASE PLEASE HELP ASAP

Answer 1

The correct answer is A. NGNGA

To find a sequence is arithmetic, we are going to find its common difference:
`d=a_(n)-a_(n-1)`
where

`d` is the common difference

`a_(n)` is the current term in the sequence

`a_(n-1)` is the previous term in the sequence
To find if a sequence is geometric, we are going to find its common ratio:

`r= (a_(n))/(a_(n-1))`
where

`r` is the common ratio

`a_(n)` is the current term in the sequence

`a_(n-1)` is the previous term in the sequence

1) 3,4,6,10,18
For
`a_(n)=4` and
`a_(n-1)=3`:

`d=a_(n)-a_(n-1)`

`d=4-3`

`d=1`
For
`a_(n)=6` and
`a_(n-1)=4`:

`d=6-4`

`d=2`

For
`a_(n)=4` and
`a_(n-1)=3`:

`r= (a_(n))/(a_(n-1))`

`r= (4)/(3)`
For
`a_(n)=6` and
`a_(n-1)=4`:

`r= (6)/(4)`

`r= (3)/(2)`
We can conclude that the sequence is neither arithmetic nor geometric.

2)
`(25)/(4) , (5)/(2) ,1...`
For
`a_(n)= (5)/(2)` and
`a_(n-1)= (25)/(4)`:

`d=a_(n)-a_(n-1)`

`d=(5)/(2)-(25)/(4)`

`d=- (15)/(4)`
For
`a_(n)=1` and
`a_(n-1)= (5)/(2)`:

`d= 1-(5)/(2)`

`d= -(3)/(2)`

For
`a_(n)= (5)/(2)` and
`a_(n-1)= (25)/(4)`:

`r= (a_(n))/(a_(n-1))`

`r= ((5)/(2) )/((25)/(4) )`

`r= (2)/(5)`
For
`a_(n)=1` and
`a_(n-1)= (5)/(2)`:

`r= (1)/((5)/(2))`

`r= (2)/(5)`
We have a common ratio, we can conclude that the sequence is geometric.

3)
`(2)/(3) , (4)/(6) , (8)/(9) ...`
For
`a_(n)=(4)/(6)` and
`a_(n-1)= (2)/(3)`:

`d=(4)/(6)-(2)/(3)`

`d=0`

For
`a_(n)=(4)/(6)` and
`a_(n-1)= (2)/(3)`:

`r= ((4)/(6))/((2)/(3))`

`r=1`
For
`a_(n)=(8)/(9)` and
`a_(n-1)= (4)/(6)`:

`r= ((8)/(9))/((4)/(6))`

`r= (4)/(3)`
We can conclude that the sequence is neither arithmetic nor geometric.

4) 3,15,75...
For
`a_(n)=15` and
`a_(n-1)=3`:

`d=15-3`

`d=12`
For
`a_(n)=75` and
`a_(n-1)=15`:

`d=75-15`

`d=60`

For
`a_(n)=15` and
`a_(n-1)=3`:

`r= (15)/(3)`

`r=5`
For
`a_(n)=75` and
`a_(n-1)=15`:

`r= (75)/(15)`

`r=5`
We have a common ratio, we can conclude that the sequence is geometric.

5) 5,-11,-27
For
`a_(n)=-11` and
`a_(n-1)=5`:

`d=-11-5`

`d=-16`
For
`a_(n)=-27` and
`a_(n-1)=-11`:

`d=-27--11`

`d=-27+11`

`d=-16`
We have a common difference, we can conclude that the sequence is arithmetic.