Answer:
1,4,9,16,25
Step-by-step explanation:
We have been given the formula [tex]a_1=1\text{and}a_n=a_{n-1}+(2n-1)[/tex]
Substitute n=2 in given recursive formula
[tex]a_2=a_1+(2\cdot2-1)[/tex]
[tex]a_2=1+(3)[/tex]
[tex]a_2=4[/tex]
Substitute n=3 in given recursive formula
[tex]a_3=a_2+(2\cdot 3-1)[/tex]
[tex]a_3=4+(5)[/tex]
[tex]a_3=9[/tex]
Substitute n=4 in given recursive formula
[tex]a_4=a_3+(2\cdot 4-1)[/tex]
[tex]a_4=9+(7)[/tex]
[tex]a_4=16[/tex]
Substitute n=5 in given recursive formula
[tex]a_5=a_4+(2\cdot 5-1)[/tex]
[tex]a_5=16+(9)[/tex]
[tex]a_5=25[/tex]
Hence, the first five square numbers are:
1,4,9,16,25,.....
