In a geometric sequence, each term is obtained by multiplying the previous term by a constant called the common ratio. In this case, we have the first term as 50 and the second term as 450.
To find the missing term, we first need to determine the common ratio. We can calculate the common ratio by dividing the second term by the first term:
Common Ratio (r) = Second Term / First Term
So, r = 450 / 50 = 9.
This means that each term in our sequence is obtained by multiplying the previous term by 9. Now, if we denote the missing term as ‘x’, we can express the sequence as follows:
- First term: 50
- Missing term: x
- Second term: 450
Since the second term can also be expressed in terms of the first term and the common ratio, we have:
x = First Term * r = 50 * 9 = 450.
However, to find the missing term that lies between these terms, we need to see how this can fit into the sequence. The missing term would logically have to be:
x = 50 * r = 50 * 9 = 450.
Since we already know 450 is a term, we know there isn’t a valid middle term in this specific case (as there is no term between 50 and 450 using a simple constant multiplication, where the common ratio stands at 9). But for similar scenarios involving other numbers, the missing term could also potentially be found using:
For example, if you’re looking for a situation where we have a third term to consider:
First term: 50
Missing term: 50 * 3 (for example, if the common ratio were different).
In conclusion, a common ratio can dramatically affect how the missing term behaves and is determined. In this case, while mathematically, 450 does not indicate a mid-value in a standard sequence from 50, it serves to illustrate the nuance of interpreting geometric progressions. Hence, if you need a possible term systematically, you’d have:
The solution can yield varied values based on defined parameters and the significance of what ‘missing term’ represents in broader sequences.