Determine whether the sequence is geometric. If it is, find the common ratio.

Question

anonymous · Answer

a)$$-1,1,-1,1,...$$
b) $$1, \frac{ 1 }{ 2 },\frac{ 1 }{ 3 },\frac{ 1 }{ 4 },...$$

anonymous · Answer

Use the rule outlined in my attachment hereto.  Plug in the given values for each sequence to determine whether it  a geometric sequence.

anonymous · Answer

I dont understand, can you work A and I will see what you do?

campbell_st · Answer

well to find the common ratio compare the terms 

if you have 

$$a_{1}, a_{2}, a_{3}, a_{4} .....$$

look at the ratios, does

$$\frac{a_{2}}{a_{1}} = \frac{a_{3}}{a_{2}} = \frac{a_{4}}{a_{3}}....$$

so in you're 1st question does 

$$\frac{-1}{1} = \frac{1}{-1} = \frac{-1}{1}.....$$

if the answer is yes or true... then you have a geometric sequence... 

hope it helps

anonymous · Answer

it is a geometric sequence, thats what I got. and the common ratio is 1?

campbell_st · Answer

not quite, it is geometric... but the common ratio is -1.... 

that why the sign of each term changes... 

so in the 2nd question does

$$\frac{\frac{1}{2}}{1} = \frac{\frac{1}{3}}{\frac{1}{2}} = ...$$

if it yes... its geometric... if now... its not...

campbell_st · Answer

oops no.... rather that now

anonymous · Answer

Alright, for B. It is not geometric. Is that correct?