If a_(1)=2 and a_(n+1)=(a_(n))^(2)+5 then find the value of a_(4). Answer:

Given terms and formula: We are given the first term of the sequence, a_(1) = 2, and the recursive formula for the sequence, a_(n+1) = (a_(n))^2 + 5. We need to find the value of the fourth term, a_(4).Calculate a_(2): To find a_(2), we use the recursive formula with n = 1: a_(2) = (a_(1))^2 + 5. Calculation: a_(2) = (2)^2 + 5 = 4 + 5 = 9.Calculate a_(3): Next, we find a_(3) using the recursive formula with n = 2: a_(3) = (a_(2))^2 + 5. Calculation: a_(3) = (9)^2 + 5 = 81 + 5 = 86.Calculate a_(4): Finally, we find a_(4) using the recursive formula with n = 3: a_(4) = (a_(3))^2 + 5. Calculation: a_(4) = (86)^2 + 5 = 7396 + 5 = 7401.

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If
a_(1)=2 and
a_(n+1)=(a_(n))^(2)+5 then find the value of
a_(4).
Answer:

If $a_{1}=2$ and $a_{n+1}=\left(a_{n}\right)^{2}+5$ then find the value of $a_{4}$ . $\newline$ Answer:

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Algebra 2

Evaluate rational expressions II

Full solution

Q. If

a_{1}=2

and

a_{n+1}=\left(a_{n}\right)^{2}+5

then find the value of

a_{4}

\newline

Answer:

Given terms and formula: We are given the first term of the sequence, $a_{1} = 2$ , and the recursive formula for the sequence, $a_{n+1} = (a_{n})^2 + 5$ . We need to find the value of the fourth term, $a_{4}$ .
Calculate $a_{2}$ : To find $a_{2}$ , we use the recursive formula with $n = 1$ : $a_{2} = (a_{1})^2 + 5$ . $\newline$ Calculation: $a_{2} = (2)^2 + 5 = 4 + 5 = 9$ .
Calculate $a_{3}$ : Next, we find $a_{3}$ using the recursive formula with $n = 2$ : $a_{3} = (a_{2})^2 + 5$ . $\newline$ Calculation: $a_{3} = (9)^2 + 5 = 81 + 5 = 86$ .
Calculate $a_{4}$ : Finally, we find $a_{4}$ using the recursive formula with $n = 3$ : $a_{4} = (a_{3})^2 + 5$ . $\newline$ Calculation: $a_{4} = (86)^2 + 5 = 7396 + 5 = 7401$ .