Answer:
The general th term of the sequence is [tex]\frac{6n-1}{3}[/tex]
Step-by-step explanation:
1.Identify the pattern in the sequence:
Remove the common denominator to focus on the numerators:
5,11,17,23,…
2. Find the differences between consecutive terms:
11−5=6
17−11=6
23−17=6
3. Determine the general term for the arithmetic sequence:
The general term of an arithmetic sequence can be written as:
"an=a1+(n−1)d"
where 1 is the first term and is the common difference. Here, 1= 5 and = 6. So the -th term of the arithmetic sequence is:
" = 5 + ( − 1 ) ⋅ 6 "
Simplify this:
= 5 + 6 ( − 1 )
= 5 + 6 − 6
= 6 − 1
4. Since the original sequence has a common denominator of 3 divide the term by 3:
General th = [tex]\frac{6n-1}{3}[/tex]
