Respuesta :
Given:
[tex]a_n=a_{n-1}+3[/tex]
[tex]a_0=2[/tex]
To find:
The values [tex]a_1,a_2,a_3[/tex].
Solution:
We have,
[tex]a_n=a_{n-1}+3[/tex]
For [tex]n=1[/tex],
[tex]a_1=a_{1-1}+3[/tex]
[tex]a_1=a_{0}+3[/tex]
[tex]a_1=2+3[/tex]
[tex]a_1=5[/tex]
For [tex]n=2[/tex],
[tex]a_2=a_{2-1}+3[/tex]
[tex]a_2=a_{1}+3[/tex]
[tex]a_2=5+3[/tex]
[tex]a_2=8[/tex]
For [tex]n=3[/tex],
[tex]a_3=a_{3-1}+3[/tex]
[tex]a_3=a_{2}+3[/tex]
[tex]a_3=8+3[/tex]
[tex]a_3=11[/tex]
Therefore, [tex]a_1=5,a_2=8,a_3=11[/tex].
The value of [tex]\rm a_1=5[/tex], [tex]\rm a_2=8[/tex], and [tex]\rm a_3=11[/tex] and this can be determined by using the arithmetic operations and the given data.
Given :
Let {an} be a sequence that satisfies the recurrence relation [tex]\rm a_n=a_{n-1}+3[/tex] for n = 1, 2, 3,... and suppose that [tex]\rm a_0=2[/tex].
According to the given data, the recurrence relation is given below:
[tex]\rm a_n=a_{n-1}+3[/tex] --- (1)
Now, substitute the value of (n = 1) in the above expression.
[tex]\rm a_1=a_{1-1}+3[/tex]
[tex]\rm a_1=a_{0}+3[/tex] (put [tex]\rm a_0=2[/tex])
[tex]\rm a_1=2+3[/tex]
[tex]\rm a_1=5[/tex]
Now, substitute the value of (n = 2) in the expression (1).
[tex]\rm a_2=a_{2-1}+3[/tex]
[tex]\rm a_2=a_{1}+3[/tex] (put [tex]\rm a_1=5[/tex])
[tex]\rm a_2=5+3[/tex]
[tex]\rm a_2=8[/tex]
Now, substitute the value of (n = 3) in the expression (1).
[tex]\rm a_3=a_{3-1}+3[/tex]
[tex]\rm a_3=a_{2}+3[/tex] (put [tex]\rm a_2=8[/tex])
[tex]\rm a_3=8+3[/tex]
[tex]\rm a_3=11[/tex]
For more information, refer to the link given below:
https://brainly.com/question/10168678
