For the sequence, describe the pattern, write the next term, and write a rule for the nth term.

2/3,4/4,6/5,8/6,...

i think its 10/7

To analyze the given sequence 2/3, 4/4, 6/5, 8/6,..., we can observe the following pattern:

- The numerator of each fraction increases by 2 in each consecutive term: starting with 2, then 4, then 6, and so on.
- The denominator of each fraction increases by 1 in each consecutive term: starting with 3, then 4, then 5, and so on.

Based on this pattern, we can determine the next term in the sequence:

The next term will have a numerator of 10 because it follows the pattern of increasing by 2 (8 + 2 = 10).
The next term will have a denominator of 7 because it follows the pattern of increasing by 1 (6 + 1 = 7).

Therefore, the next term in the sequence is 10/7.

To find a rule for the nth term of the sequence, we can observe that the numerator of each term is equal to 2 multiplied by the corresponding index (n), and the denominator is equal to the index (n) increased by 1:

Numerator: 2 * n
Denominator: n + 1

So, the rule for the nth term in the sequence is:

Nth term = (2 * n) / (n + 1)

For example:
- The 1st term (n = 1) is (2 * 1) / (1 + 1) = 2 / 2 = 1.
- The 2nd term (n = 2) is (2 * 2) / (2 + 1) = 4 / 3 ≈ 1.333.
- The 3rd term (n = 3) is (2 * 3) / (3 + 1) = 6 / 4 = 1.5.

This rule can be used to find any term in the sequence by substituting the desired value for n.