The recursive formula is: [tex]a_n = a_{n-1} + \frac{2}{3}[/tex]
Step-by-step explanation:
A recursive formula is used to find the next term of a sequence using the previous term and common difference
Given sequence is:
{3,11/3,13/3,5,17/3...}
Here,
[tex]a_1 = 3\\a_2 = \frac{11}{3}\\a_3 = \frac{13}{3}\\a_4 = 5[/tex]
Now,
[tex]d = a_2-a_1 = \frac{11}{3} - 3 = \frac{11-9}{3} = \frac{2}{3}\\d = a_3 - a_2 = \frac{13}{3} - \frac{11}{3} = \frac{13-11}{3} = \frac{2}{3}[/tex]
Hence,
The common difference is: 2/3
So,
The recursive formula is generally given by:
[tex]a_n = a_{n-1} + d[/tex]
Putting the value of d
[tex]a_n = a_{n-1} + \frac{2}{3}[/tex]
Hence,
The recursive formula is: [tex]a_n = a_{n-1} + \frac{2}{3}[/tex]
Keywords: Sequence, common difference
Learn more about sequences at:
- brainly.com/question/3799248
- brainly.com/question/3950386
#LearnwithBrainly
