SOLUTION: Find the missing terms in each geometric sequence. 1. ___,___,-16,4,-1 2. 625,___,25,___,1 3. 0.3,___,2.7,___,___. 4. -1/3,___,-4/45,___,8/135,___. It's okay if there's

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Question 1186017: Find the missing terms in each geometric sequence.
1. ___,___,-16,4,-1
2. 625,___,25,___,1
3. 0.3,___,2.7,___,___.
4. -1/3,___,-4/45,___,8/135,___.

It's okay if there's no solution please help.
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
1. ___,___,-16,4,-1

4 over -16 is -4/16 which reduces the -1/4
-1 over 4 is also -1/4
So the blank left of 16 is something so that if you multiply it by -1/4
you get -16.  If it is x then


Can you solve that?

If you can, then the first blank is something so that if you multiply it by -1/4
you get what you got for the second blank. 


2. 625,___,25,___,1

If the common ratio is r, the  goes in the second blank

   625, 625r,25,___,1

So (625r)(r)=25
       625r2=25
          r2=25/625
           r=5/25
           r=1/5

So what does 625r equal?

Multiply 25 by r to get what goes in the other blank

3. 0.3,___,2.7,___,___.

That's the same way as 2, except it uses decimals instead of fractions.

4. -1/3,___,-4/45,___,8/135,___.

You can do that one.

Edwin
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.

In part (2), the ratio of the third term to the first term gives you 

    r^2 = ,


which gives TWO possible values for the common ratio  r =   and  r = .


They have  EQUAL RIGHTS  and produce  TWO possible geometric sequences.


One sequence is        625,  125,  25,  5,  1.


The other sequence is  625, -125,  25, -5,  1.


So, there are two answers and two possible geometric sequences, instead of one,
as proclaimed by @Edwin.




Similar notice goes to part (3).




Regarding part (4),  it is not geometric sequence, at all.

So, you  ONLY CAN  reject it . . .



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