If a_(1)=2 and a_(n)=(a_(n-1))^(2)-3 then find the value of a_(4). Answer:

Given Sequence and Formula: We are given the first term of the sequence, a_(1) = 2, and the recursive formula for the sequence, a_(n) = (a_(n-1))^2 - 3. We need to find the value of the fourth term, a_(4).Find Second Term: First, let's find the second term, a_(2), using the recursive formula with n=2. a_(2) = (a_(1))^2 - 3 Substitute a_(1) = 2 into the formula. a_(2) = (2)^2 - 3Calculate a_(2): Calculate the value of a_(2). a_(2) = 4 - 3 a_(2) = 1Find Third Term: Next, let's find the third term, a_(3), using the recursive formula with n=3. a_(3) = (a_(2))^2 - 3 Substitute a_(2) = 1 into the formula. a_(3) = (1)^2 - 3Calculate a_(3): Calculate the value of a_(3). a_(3) = 1 - 3 a_(3) = -2Find Fourth Term: Finally, let's find the fourth term, a_(4), using the recursive formula with n=4. a_(4) = (a_(3))^2 - 3 Substitute a_(3) = -2 into the formula. a_(4) = (-2)^2 - 3Calculate a_(4): Calculate the value of a_(4). a_(4) = 4 - 3 a_(4) = 1

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Algebra 2

Evaluate rational expressions II

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Q. If

a_{1}=2

and

a_{n}=\left(a_{n-1}\right)^{2}-3

then find the value of

a_{4}

\newline

Answer:

Given Sequence and Formula: We are given the first term of the sequence, $a_{1} = 2$ , and the recursive formula for the sequence, $a_{n} = (a_{n-1})^2 - 3$ . We need to find the value of the fourth term, $a_{4}$ .
Find Second Term: First, let's find the second term, $a_{2}$ , using the recursive formula with $n=2$ . $\newline$ $a_{2} = (a_{1})^2 - 3$ $\newline$ Substitute $a_{1} = 2$ into the formula. $\newline$ $a_{2} = (2)^2 - 3$
Calculate $a_{2}$ : Calculate the value of $a_{2}$ . $a_{2} = 4 - 3$ $a_{2} = 1$
Find Third Term: Next, let's find the third term, $a_{3}$ , using the recursive formula with $n=3$ . $\newline$ $a_{3} = (a_{2})^2 - 3$ $\newline$ Substitute $a_{2} = 1$ into the formula. $\newline$ $a_{3} = (1)^2 - 3$
Calculate $a_{3}$ : Calculate the value of $a_{3}$ . $a_{3} = 1 - 3$ $a_{3} = -2$
Find Fourth Term: Finally, let's find the fourth term, $a_{4}$ , using the recursive formula with $n=4$ . $\newline$ $a_{4} = (a_{3})^2 - 3$ $\newline$ Substitute $a_{3} = -2$ into the formula. $\newline$ $a_{4} = (-2)^2 - 3$
Calculate $a_{4}$ : Calculate the value of $a_{4}$ . $\newline$ $a_{4} = 4 - 3$ $\newline$ $a_{4} = 1$