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Find the general nth term of 5/3, 11/3, 17/3 23/3​

Find The General Nth Term Of 53 113 173 233 class=

Sagot :

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]