Question

Let {an} be a sequence that satisfies the recurrence relation an = an-1 + 3 for n = 1, 2, 3, ... , and suppose that a0 = 2. What are a1, a2, and a3? Show your solution.

Answer 1

Given:

$a_n=a_{n-1}+3$

$a_0=2$

To find:

The values $a_1,a_2,a_3$.

Solution:

We have,

$a_n=a_{n-1}+3$

For $n=1$,

$a_1=a_{1-1}+3$

$a_1=a_{0}+3$

$a_1=2+3$

$a_1=5$

For $n=2$,

$a_2=a_{2-1}+3$

$a_2=a_{1}+3$

$a_2=5+3$

$a_2=8$

For $n=3$,

$a_3=a_{3-1}+3$

$a_3=a_{2}+3$

$a_3=8+3$

$a_3=11$

Therefore, $a_1=5,a_2=8,a_3=11$.