The formula for sn is [tex]S_n = \frac{2 + n}{2 + 3n}[/tex] where n≥1
The list is given as:
3/5,4/8,5/11,6/14,7/17,…
The above list is a sequence of fractions, where the difference between adjacent numerators is 1, and the difference between adjacent denominator is 3.
The first term of the sequence is:
[tex]S_1 = \frac{3}{5}[/tex]
Rewrite as:
[tex]S_1 = \frac{2 + 1}{2 + 3}[/tex]
Express 1 and 3 as product
[tex]S_1 = \frac{2 + 1 * 1}{2 + 3 * 1}[/tex]
Substitute n for 1
[tex]S_n = \frac{2 + 1 * n}{2 + 3 * n}[/tex]
Evaluate the product
[tex]S_n = \frac{2 + n}{2 + 3n}[/tex]
Hence, the formula for sn is [tex]S_n = \frac{2 + n}{2 + 3n}[/tex]
Read more about sequence at:
https://brainly.com/question/6561461
