Question

Is there a common ratio for the geometric sequence and what are the missing terms?

16,40,100,?,?

IS there a common ratio for the geometric sequence and what are the missing terms?

81,54,?,?,?

Answer 1

Yes, and 2.5 is the ratio. Following terms are 150, and 225.

For the second question, try 2/3 for the ratio. 36, 24, ...
With only two terms, one really can't say if there is a "common" ratio. There are no other pairs to compare.

Answer 2

if the given sequence is a geometric sequence, then it follows the formula
A,n+1 = r*(A,n)
where
r = ratio between two consecutive terms
A,n = the nth term
A,n+1 = the term after A,n

substituting the first and second term,
40 = r*16
r = 40/16
r = 2.5
to check, let's see if we would obtain 100 if we multiply 40 by the ratio=2.5
40*2.5 = 100
to find the next term after 100, we just multiply by the ratio,, thus the next two terms are:
100*2.5 = 250
250*2.5 = 625

for the second question, if it's a geometric sequence, then it follows the formula above. thus, getting the ratio,
54 = r*81
r = 54/81
r = 2/3
to get the next three terms, we multiply the next terms by 2/3:
54*(2/3) = 36
36*(2/3) = 24
24*(2/3) = 16

hope this helps~ :)