Question

Write a pseudocode for the given recurrence relation below to

calculate an, where n can be any positive integer.
a1 = a2 = 1
an =2an-1 -3an-2

Answer 1

The requested pseudocode defines a function to calculate terms of a sequence defined by a recurrence relation. It includes base cases for the sequence and iteratively computes subsequent terms using the given relation.

Step-by-step explanation:

The student is asking for a pseudocode to calculate the sequence defined by the recurrence relation a1 = a2 = 1 and an = 2an-1 - 3an-2, where n is any positive integer. Below is the pseudocode to calculate an.

function calculate_a(n):
if n == 1 or n == 2:
return 1
else:
a_n_minus_1 = 1
a_n_minus_2 = 1
for i from 3 to n:
a_n = 2 * a_n_minus_1 - 3 * a_n_minus_2
a_n_minus_2 = a_n_minus_1
a_n_minus_1 = a_n
return a_n

This pseudocode sets the base cases for the first two terms and then uses iteration to calculate subsequent terms according to the given recurrence relation.