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: 
$r= \frac{a_{n}}{a_{n-1}}$
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 $a_{n-1}=3$:
$r= \frac{a_{n}}{a_{n-1}}$
$r= \frac{4}{3}$
For $a_{n}=6$ and $a_{n-1}=4$:
$r= \frac{6}{4}$
$r= \frac{3}{2}$
We can conclude that the sequence is neither arithmetic nor geometric.

2) $\frac{25}{4} , \frac{5}{2} ,1...$
For $a_{n}= \frac{5}{2}$ and $a_{n-1}= \frac{25}{4}$:
$d=a_{n}-a_{n-1}$
$d=\frac{5}{2}-\frac{25}{4}$
$d=- \frac{15}{4}$
For $a_{n}=1$ and $a_{n-1}= \frac{5}{2}$:
$d= 1-\frac{5}{2}$
$d= -\frac{3}{2}$

For $a_{n}= \frac{5}{2}$ and $a_{n-1}= \frac{25}{4}$:
$r= \frac{a_{n}}{a_{n-1}}$
$r= \frac{\frac{5}{2} }{\frac{25}{4} }$
$r= \frac{2}{5}$
For $a_{n}=1$ and $a_{n-1}= \frac{5}{2}$:
$r= \frac{1}{\frac{5}{2}}$
$r= \frac{2}{5}$
We have a common ratio, we can conclude that the sequence is geometric.

3) $\frac{2}{3} , \frac{4}{6} , \frac{8}{9} ...$
For $a_{n}=\frac{4}{6}$ and $a_{n-1}= \frac{2}{3}$:
$d=\frac{4}{6}-\frac{2}{3}$
$d=0$ 

For $a_{n}=\frac{4}{6}$ and $a_{n-1}= \frac{2}{3}$:
$r= \frac{\frac{4}{6}}{\frac{2}{3}}$
$r=1$
For $a_{n}=\frac{8}{9}$ and $a_{n-1}= \frac{4}{6}$:
$r= \frac{\frac{8}{9}}{\frac{4}{6}}$
$r= \frac{4}{3}$
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 $a_{n-1}=3$:
$r= \frac{15}{3}$
$r=5$
For $a_{n}=75$ and $a_{n-1}=15$:
$r= \frac{75}{15}$
$r=5$
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.