Question

The square numbers can be defined by the recursive formula a1 = 1, and an = an-1 + (2n - 1), where n > 1. The first five square numbers are

Answer 1

1,4,9,16,25

Explanation:

We have been given the formula
`a_1=1\text{and}a_n=a_(n-1)+(2n-1)`

Substitute n=2 in given recursive formula

`a_2=a_1+(2\cdot2-1)`

`a_2=1+(3)`

`a_2=4`

Substitute n=3 in given recursive formula

`a_3=a_2+(2\cdot 3-1)`

`a_3=4+(5)`

`a_3=9`

Substitute n=4 in given recursive formula

`a_4=a_3+(2\cdot 4-1)`

`a_4=9+(7)`

`a_4=16`

Substitute n=5 in given recursive formula

`a_5=a_4+(2\cdot 5-1)`

`a_5=16+(9)`

`a_5=25`

Hence, the first five square numbers are:

1,4,9,16,25,.....