The value of a3 for the given recursive pattern is 446
A sequence can either follow an arithmetic progression or geometric progression or none
The given parameters are:
[tex]a_1 = 4[/tex]
[tex]a_n = (a_{n-1})^2 + 5[/tex]
Start by calculating a2
[tex]a_2 = (a_{2-1})^2 + 5[/tex]
[tex]a_2 = (a_1)^2 + 5[/tex]
Substitute 4 for a1
[tex]a_2 = 4^2 + 5[/tex]
[tex]a_2 = 21[/tex]
Next, calculate a3
[tex]a_3 = (a_{3-1})^2 + 5[/tex]
[tex]a_3 = (a_{2})^2 + 5[/tex]
Substitute 21 for a2
[tex]a_3 = 21^2 + 5[/tex]
[tex]a_3 = 446[/tex]
Hence, the value of a3 is 446
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