Is there a common ratio for the geometric sequence and what are the missing terms?
2, -4, -16, -36..
No common ratio, thus no geometric sequence
however the 2nd, 3rd and 4th form the pattern:
-(consecutive even)^2
but then the first term does not follow this pattern.
I don't see anything else
Thank you @Reiny
Yes, there is a common ratio for a geometric sequence. To find the common ratio, you divide any term in the sequence by its preceding term. Let's calculate it for the given sequence:
-4 ÷ 2 = -2
-16 ÷ -4 = 4
-36 ÷ -16 = 2.25
We can see that the ratio is not consistent, as it changes from -2 to 4 and then to 2.25. Therefore, this sequence does not have a common ratio.
To find the missing terms in a geometric sequence, we need to determine the pattern followed by the existing terms. Looking at the given sequence, we can observe that each term is obtained by multiplying the preceding term by a decreasing value. For example, 2 × (-2) = -4, -4 × (-4) = -16, and so on.
Using this pattern, we can calculate the missing terms:
-16 × (-2) = 32
32 × (-4) = -128
-128 × (-2) = 256
Therefore, the missing terms in the sequence are 32, -128, and 256.