Using the given information, the value of [tex]a_{4}[/tex] is 7401
From the question, we are to determine the value of [tex]a_{4}[/tex]
From the given information,
[tex]a_{n} = (a_{n-1})^{2} +5[/tex]
Then we can write that
[tex]a_{4} = (a_{3})^{2}+5[/tex]
[tex]a_{3} = (a_{2})^{2}+5[/tex]
[tex]a_{2} = (a_{1})^{2}+5[/tex]
Also, from the given information
[tex]a_{1} = 2[/tex]
Then,
[tex]a_{2} = (a_{1})^{2}+5[/tex] becomes
[tex]a_{2} = (2)^{2}+5[/tex]
[tex]a_{2} = 4+5[/tex]
[tex]a_{2} = 9[/tex]
Also,
[tex]a_{3} = (a_{2})^{2}+5[/tex] becomes
[tex]a_{3} = (9)^{2}+5[/tex]
[tex]a_{3} = 81+5[/tex]
[tex]a_{3} = 86[/tex]
Then,
[tex]a_{4} = (a_{3})^{2}+5[/tex] becomes
[tex]a_{4} = (86)^{2}+5[/tex]
[tex]a_{4} = 7396 +5[/tex]
[tex]a_{4} = 7401[/tex]
Hence, the value of [tex]a_{4}[/tex] is 7401
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