We know that:
[tex]a_n=1[/tex]and
[tex]a_n=(a_{n-1})^2+5[/tex]To find the value of a3 we need to find the value of a2 first:
[tex]a_2=(a_{2-1})^2+5=(a_1)^2+5=(1)^2+5=1+5=6[/tex]Then:
[tex]a_3=(a_{3-1})^2+5=(a_2)^2+5=(6)^2+5=36+5=41[/tex]Therefore:
[tex]a_3=41[/tex]