Coleman Hart
04/22/2024 · Senior High School

Find the indicated term of the Fibonacci Sequence \( 9^{\text {th }} \) term

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The Fibonacci sequence is defined as follows: - \( F(0) = 0 \) - \( F(1) = 1 \) - For \( n \geq 2 \), \( F(n) = F(n-1) + F(n-2) \) To find the \( 9^{\text{th}} \) term, we can calculate the terms of the sequence up to \( F(9) \): - \( F(0) = 0 \) - \( F(1) = 1 \) - \( F(2) = F(1) + F(0) = 1 + 0 = 1 \) - \( F(3) = F(2) + F(1) = 1 + 1 = 2 \) - \( F(4) = F(3) + F(2) = 2 + 1 = 3 \) - \( F(5) = F(4) + F(3) = 3 + 2 = 5 \) - \( F(6) = F(5) + F(4) = 5 + 3 = 8 \) - \( F(7) = F(6) + F(5) = 8 + 5 = 13 \) - \( F(8) = F(7) + F(6) = 13 + 8 = 21 \) - \( F(9) = F(8) + F(7) = 21 + 13 = 34 \) Thus, the \( 9^{\text{th}} \) term of the Fibonacci sequence is \( F(9) = 34 \).

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The \( 9^{\text{th}} \) term of the Fibonacci sequence is 34.
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