[tex]a_n=a_{n-1}+3=a_{n-2}+2\cdot3=a_{n-3}+3\cdot3=\cdots=a_0+n\cdot3[/tex]
[tex]a_n=3n+1[/tex]
The solution of the recurrence relation [tex]a_n = a_{n-1} + 3[/tex] is given by [tex]a_n = 3n + 1[/tex] and this can be determined by using the arithmetic operations.
Given :
In order to determine the solution of the recurrence relation, substitute (n = 1) in the given relation.
[tex]a_1 = a_{1-1} + 3[/tex]
[tex]a_1 = a_{0} + 3[/tex]
[tex]a_1 = 1 + 3[/tex]
[tex]a_1 = 4[/tex]
Now, substitute the value of (n = 2) in the given relation.
[tex]a_2 = a_{1} + 3[/tex]
[tex]a_2 = 4 + 3[/tex]
[tex]a_2 = 7[/tex]
Now, substitute the value of (n = 3) in the given relation.
[tex]a_3 = a_{2} + 3[/tex]
[tex]a_3 = 7 + 3 = 10[/tex]
So, from the above calculation, it can be concluded that the solution of the recurrence relation [tex]a_n = a_{n-1} + 3[/tex] is given by:
[tex]a_n = 3n + 1[/tex]
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https://brainly.com/question/15385899
