Is there a common ratio for the geometric sequence and what are the missing terms?
2, -4, -16, -36..
Yes, there is a common ratio in a geometric sequence. To find the common ratio, we divide any term in the sequence by its previous term.
Let's check the common ratio for this geometric sequence:
-4 / 2 = -2
-16 / -4 = 4
-36 / -16 = 2.25
As we can see, the ratios are not consistent. Therefore, this sequence does not have a common ratio. It is not a geometric sequence.
To find the missing terms in the sequence, we need to understand the pattern or rule that the sequence follows. Without a specified pattern, it is difficult to determine the missing terms with certainty. However, we can make an educated guess based on the given terms.
In the given sequence, we notice that each term is obtained by adding a certain number to its preceding term, and the added number increases by multiples of 4.
Using this observation, we can attempt to find the missing terms. Continuing the pattern:
-36 + (-4) = -40
-40 + (-8) = -48
-48 + (-12) = -60
Therefore, the missing terms in the sequence are: -40, -48, -60.