Question

The first few square numbers are 1,4,9, and 16. Find and solve a recurrence relation for the nth square

Answer 1

The recurrence relation for the nth square is a_n = a_n-1 + 2n - 1. By plugging in the values of n starting from 1, we can find the nth square.

Step-by-step explanation:

The recurrence relation for the nth square can be defined as:

an = an-1 + 2n - 1

To solve this recurrence relation, we can use the initial condition that a1 = 1 (since the first square is 1).

Using this recurrence relation, we can find the nth square by plugging in the values of n starting from 1:

a1 = 1

a2 = a1 + 2(2) - 1 = 4

a3 = a2 + 2(3) - 1 = 9

a4 = a3 + 2(4) - 1 = 16

and so on...