Find the next three terms in the
following geometric sequence.
4, −12, 36, −108,…
To find the next term in a geometric sequence, we need to multiply the previous term by the common ratio.
The common ratio can be found by dividing any term by its previous term.
For example, to find the common ratio between the second term (-12) and the first term (4), we divide -12 by 4:
-12/4 = -3
So the common ratio is -3.
To find the next term in the sequence, we multiply the last term (−108) by the common ratio:
−108 * -3 = 324
Therefore, the next term in the sequence is 324.
To find the next two terms, we continue multiplying by the common ratio:
324 * -3 = -972
-972 * -3 = 2916
So the next two terms in the sequence are -972 and 2916.
To find the next terms in the geometric sequence, we need to determine the common ratio first.
We can calculate the common ratio by dividing any term in the sequence by its preceding term. Let's take the second and first terms:
Common ratio = (-12) / 4 = -3
Now that we have the common ratio, we can find the next terms in the sequence by multiplying each term by the common ratio.
Fourth term = (-108) * (-3) = 324
Fifth term = 324 * (-3) = -972
Sixth term = -972 * (-3) = 2916
So, the next three terms in the sequence are 324, -972, and 2916.
To find the next three terms in the geometric sequence 4, -12, 36, -108, we need to identify the common ratio and continue the pattern.
A geometric sequence is a sequence in which each term is found by multiplying the previous term by a constant called the common ratio.
To find the common ratio, we divide any term by the previous term.
-12 / 4 = -3
36 / -12 = -3
-108 / 36 = -3
We can see that the common ratio is -3.
To find the next term, we multiply the last term (-108) by the common ratio (-3):
-108 * -3 = 324
Therefore, the next term in the sequence is 324.
To find the second next term, we multiply the last term (-108) by the common ratio again:
-108 * -3 * -3 = 972
Therefore, the second next term in the sequence is 972.
To find the third next term, we continue the pattern by multiplying the last term (-108) by the common ratio once more:
-108 * -3 * -3 * -3 = 2916
Therefore, the third next term in the sequence is 2916.
In summary, the next three terms in the given geometric sequence are 324, 972, and 2916.