SOLUTION: Find the missing term of each geometric sequence. 26. 16, [?] , 4 27. 25, [?] , 225 28. 2, [?] , 50 29. 1, [?] , 49 30. 3/4, [?] , 3 31. 36, [?] , 4

Algebra ->  Sequences-and-series -> SOLUTION: Find the missing term of each geometric sequence. 26. 16, [?] , 4 27. 25, [?] , 225 28. 2, [?] , 50 29. 1, [?] , 49 30. 3/4, [?] , 3 31. 36, [?] , 4      Log On


   



Question 195098: Find the missing term of each geometric sequence.
26. 16, [?] , 4
27. 25, [?] , 225

28. 2, [?] , 50
29. 1, [?] , 49
30. 3/4, [?] , 3
31. 36, [?] , 4

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Find the missing term of each geometric sequence.
 
16, [?] , 4 

let the missing term be x:

a%5B1%5D+=+16, a%5B2%5D=x, a%5B3%5D=4

Now use the fact that in a geometric sequence,

a%5B2%5D%2Fa%5B1%5D=a%5B3%5D%2Fa%5B2%5D

x%2F16+=+4%2Fx

Cross multiply:

x%5E2=64

sqrt%28x%5E2%29=%22+%22%2B-sqrt%2864%29

x = ±8

So that one has two possible answers, +8 and -8.

-----------------

25, [?] , 225

let the missing term be x:

a%5B1%5D+=+25, a%5B2%5D=x, a%5B3%5D=225

Now use the fact that in a geometric sequence,

a%5B2%5D%2Fa%5B1%5D=a%5B3%5D%2Fa%5B2%5D

x%2F25+=+225%2Fx

Cross multiply:

x%5E2=5625

sqrt%28x%5E2%29=%22+%22%2B-sqrt%285625%29

x = ±75

So that one has two possible answers, +75 and -75. 

-----

2, [?] , 50 

let the missing term be x:

a%5B1%5D+=+2, a%5B2%5D=x, a%5B3%5D=50

Now use the fact that in a geometric sequence,

a%5B2%5D%2Fa%5B1%5D=a%5B3%5D%2Fa%5B2%5D

x%2F2+=+50%2Fx

Cross multiply:

x%5E2=100

sqrt%28x%5E2%29=%22+%22%2B-sqrt%28100%29

x = ±10

So that one has two possible answers, +10 and -10. 

-----

1, [?] , 49 

let the missing term be x:

a%5B1%5D+=+1, a%5B2%5D=x, a%5B3%5D=49

Now use the fact that in a geometric sequence,

a%5B2%5D%2Fa%5B1%5D=a%5B3%5D%2Fa%5B2%5D

x%2F1+=+49%2Fx

Cross multiply:

x%5E2=49

sqrt%28x%5E2%29=%22+%22%2B-sqrt%2849%29

x = ±7

So that one has two possible answers, +7 and -7. 

-----

3/4, [?] , 3 

let the missing term be x:

a%5B1%5D+=+3%2F4, a%5B2%5D=x, a%5B3%5D=3

Now use the fact that in a geometric sequence,

a%5B2%5D%2Fa%5B1%5D=a%5B3%5D%2Fa%5B2%5D

x%2F%283%2F4%29+=+3%2Fx

Cross multiply:

x%5E2=%283%2F4%29%283%29

x%5E2=9%2F4

sqrt%28x%5E2%29=%22+%22%2B-sqrt%289%2F4%29

x = ±3%2F2

So that one has two possible answers, +3%2F2 and -3%2F2. 

-----

36, [?] , 4

let the missing term be x:

a%5B1%5D+=+36, a%5B2%5D=x, a%5B3%5D=4

Now use the fact that in a geometric sequence,

a%5B2%5D%2Fa%5B1%5D=a%5B3%5D%2Fa%5B2%5D

x%2F36+=+4%2Fx

Cross multiply:

x%5E2=144

sqrt%28x%5E2%29=%22+%22%2B-sqrt%28144%29

x = ±12

So that one has two possible answers, +12 and -12.

Edwin