Question

) Solve the recurrence relation
an - 20an-1 +1000,- 2 = 0;
do = 1, ay = 20.​

Answer 1

Explanation: an=5n+an-1

= 5n + 5(n-1) + … + an-2

= 5n + 5(n-1) + 5(n − 2) +…+ a1

= 5n + 5(n-1) + 5(n − 2) +…+ 4 [since, a1=4]

= 5n + 5(n-1) + 5(n − 2) +…+ 5.1 – 1

= 5(n + (n − 1)+…+2 + 1) – 1

= 5 * n(n+1)/ 2 – 1

an = 5 * n(n+1)/ 2 – 1

Now, n=64 so the answer is a64 = 10399.