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

Given Sequence and Formula: We are given the first term of the sequence as a_(1) = 1 and the recursive formula for the sequence as a_(n) = (a_(n-1))^2 + 1. We need to find the value of the fourth term, a_(4).Find Second Term: First, let's find the value of the second term, a_(2). According to the recursive formula, a_(2) = (a_(1))^2 + 1. Calculation: a_(2) = (1)^2 + 1 = 1 + 1 = 2.Find Third Term: Next, we find the value of the third term, a_(3). Using the recursive formula, a_(3) = (a_(2))^2 + 1. Calculation: a_(3) = (2)^2 + 1 = 4 + 1 = 5.Find Fourth Term: Finally, we calculate the value of the fourth term, a_(4). Using the recursive formula, a_(4) = (a_(3))^2 + 1. Calculation: a_(4) = (5)^2 + 1 = 25 + 1 = 26.

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

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

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Math Problems

Algebra 2

Evaluate rational expressions II

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Q. If

a_{1}=1

and

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

then find the value of

a_{4}

\newline

Answer:

Given Sequence and Formula: We are given the first term of the sequence as $a_{1} = 1$ and the recursive formula for the sequence as $a_{n} = (a_{n-1})^2 + 1$ . We need to find the value of the fourth term, $a_{4}$ .
Find Second Term: First, let's find the value of the second term, $a_{2}$ . According to the recursive formula, $a_{2} = (a_{1})^2 + 1$ . $\newline$ Calculation: $a_{2} = (1)^2 + 1 = 1 + 1 = 2$ .
Find Third Term: Next, we find the value of the third term, $a_{3}$ . Using the recursive formula, $a_{3} = (a_{2})^2 + 1$ . $\newline$ Calculation: $a_{3} = (2)^2 + 1 = 4 + 1 = 5$ .
Find Fourth Term: Finally, we calculate the value of the fourth term, $a_{4}$ . Using the recursive formula, $a_{4} = (a_{3})^2 + 1$ . $\newline$ Calculation: $a_{4} = (5)^2 + 1 = 25 + 1 = 26$ .