Final answer:
The sequence in decimal and mix number formats reveals that the next term after -37.5 would be -18.75 as a decimal and -18 3/4 as a mixed number.
Step-by-step explanation:
The sequence given is: -1875/8, -375/4, and -75/2. To find the pattern, let us convert each term to decimal and mixed number formats and observe any relationships between the numbers.
- -1875/8 as a decimal is -234.375 and as a mixed number is -234 3/8.
- -375/4 as a decimal is -93.75 and as a mixed number is -93 3/4.
- -75/2 as a decimal is -37.5 and as a mixed number is -37 1/2.
The pattern appears to be that each term is being divided by 2 to get the next term:
- -1875 divided by 8 equals -234.375
- -234.375 divided by 2 is -117.1875, which, if divided by 4, gives -93.75
- -93.75 divided by 2 gives -46.875, which is half of -93.75
Let's continue this pattern by dividing the last term -37.5 by 2:
- -37.5 divided by 2 equals -18.75
So, the next term in the sequence as a decimal is -18.75, and as a mixed number is -18 3/4.