Calculate R(4) where the recursively defined sequence
R is given by: R(1) = 2, R(2) = 3, and,
R(n) = R(n − 1) + 2R(n − 2) + n, n > 2
To calculate R(4) using the recursive definition, we need to find the value of the sequence R at the fourth term.
According to the recursive definition, R(n) = R(n − 1) + 2R(n − 2) + n, for n > 2.
We already know R(1) = 2 and R(2) = 3. Now we can use the recursive formula to find the subsequent terms.
R(3) = R(3 − 1) + 2R(3 − 2) + 3
= R(2) + 2R(1) + 3
= 3 + 2(2) + 3
= 3 + 4 + 3
= 10
R(4) = R(4 − 1) + 2R(4 − 2) + 4
= R(3) + 2R(2) + 4
= 10 + 2(3) + 4
= 10 + 6 + 4
= 20
Therefore, R(4) = 20.