Question

What is the next fraction in this sequence? Simplify your answer.

1/79 , 2/79 , 4/79 , 8/79 , ...

Answer 1

The sequence given is:

\[
\frac{1}{79}, \frac{2}{79}, \frac{4}{79}, \frac{8}{79}, \ldots
\]

We can observe the numerators of the fractions:

- The first term has a numerator of \(1\),
- The second term has a numerator of \(2\),
- The third term has a numerator of \(4\),
- The fourth term has a numerator of \(8\).

These numerators are \(1, 2, 4, 8\), which can also be written as powers of \(2\):

- \(1 = 2^0\)
- \(2 = 2^1\)
- \(4 = 2^2\)
- \(8 = 2^3\)

From this pattern, we can conclude that the numerator of the next term in the sequence will be \(2^4\):

\[
2^4 = 16
\]

Thus, the next term in the sequence is:

\[
\frac{16}{79}
\]

Since \(16\) and \(79\) have no common factors other than \(1\), the fraction is already in its simplest form.

Therefore, the next fraction in the sequence is:

\[
\frac{16}{79}
\]