Answer:
To find the next fraction in the sequence, let's analyze the pattern:
1. The numerator of each fraction is a power of 2: 2^1, 2^2, 2^3, 2^4.
2. The denominator of each fraction appears to be increasing as well: 3, 8, 27, 82.
Now, let's calculate the next fraction:
Numerator: 2^5 = 32
Denominator: The pattern for the denominator isn't as straightforward, but we can try to find a pattern by looking at the differences between consecutive denominators:
8 - 3 = 5
27 - 8 = 19
82 - 27 = 55
The differences between consecutive denominators don't seem to follow a simple arithmetic progression, so we can't determine the exact next denominator using a straightforward formula. However, we can continue the pattern by adding the next positive integer to 82:
82 + 1 = 83
So, the next fraction in the sequence would be:
(32/83)