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,?,?,?
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.
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~ :)
To determine if there is a common ratio for a geometric sequence, we need to check if there is a constant factor between consecutive terms.
For the sequence 16, 40, 100, ?, ?, let's find the common ratio:
To get from 16 to 40, we multiply by 2 (16 * 2 = 40).
To get from 40 to 100, we multiply by 2.5 (40 * 2.5 = 100).
Therefore, the common ratio for this geometric sequence is 2.5.
To find the missing terms, we can continue multiplying the last term by the common ratio.
100 * 2.5 = 250 (the fourth term)
250 * 2.5 = 625 (the fifth term)
So, the missing terms for the sequence 16, 40, 100, ?, ? are 250 and 625.
Now, let's move on to the second sequence: 81, 54, ?, ?, ?
To find the common ratio, we again examine the factors between consecutive terms:
To get from 81 to 54, we divide by 1.5 (81 / 1.5 = 54).
Therefore, the common ratio for this geometric sequence is 1.5.
To find the missing terms, we can either continue dividing the last term by the common ratio or multiply by the reciprocal.
54 / 1.5 = 36 (the third term)
36 / 1.5 = 24 (the fourth term)
24 / 1.5 = 16 (the fifth term)
Thus, the missing terms for the sequence 81, 54, ?, ?, ? are 36, 24, and 16.
To determine if there is a common ratio for a geometric sequence, we need to check if the ratios between consecutive terms are constant. Let's examine the given sequences:
1) 16, 40, 100, ?, ?
To find the common ratio, we can divide any term by its preceding term. Let's calculate the ratios:
40/16 = 2.5
100/40 = 2.5
Since both ratios are equal to 2.5, we can conclude that there is a common ratio of 2.5 for this geometric sequence.
To find the missing terms, we can multiply each term by the common ratio of 2.5:
100 * 2.5 = 250
250 * 2.5 = 625
Therefore, the missing terms in this sequence are 250 and 625.
2) 81, 54, ?, ?, ?
Let's calculate the ratios for this sequence:
54/81 = 0.67
?/54 = 0.67
? = 54 * 0.67
? = 36.18
Since the ratio between the second and first term is not the same as the ratio between the third and second term, we can conclude that there is no common ratio for this sequence.
To find the missing terms, we can only make assumptions based on the given terms. There is no specific pattern or common ratio that we can use to calculate the missing values in this case. Therefore, we cannot determine the exact missing terms for this sequence.