Question

Write a recursive definition for the sequence 11,8,5,2

Answer 1

$$
a_0=2\\
a_1=5=a_0+3\\
a_2=8=a_1+3\\
a_3=11=a_2+3
$$
Do you see the pattern?

So, the nth number can be found from the (n-1)st number using the formula
$$
a_0=2\\
a_i=a_{i-1}+3
$$

But we want to go backwards from 11,8, to 2 not 2 to 11, so
$$
a_0=11\\
a_1=8=a_0-3\\
a_2=5=a_1-3\\
a_3=2=a_2-3
$$

So, the nth number can be found from the (n-1)st number using the formula
$$
a_0=11\\
a_i=a_{i-1}-3
$$
Which is the recursive equation we sought.

Make sense?

Answer 2

yes sir is does thank you:)