A sequence is defined recursively by the following rules:

\[ f(1)=3 \]
\[ f(n+1)=2 \cdot f(n)-1 \]

Which of the following statements are true about the sequence? Select TWO that apply.

A. $ f(2)=5 $
B. $ f(3)=10 $
C. $ f(4)=18 $
D. $ f(5)=33 $
E. $ f(6)=66 $

We will check the value of the sequence given by each option

f₂ = f₁₊₁ = 2(f₁) - 1 = 2(3) - 1 = 6 - 1 = 5

Option A is correct
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f₃ = f₂₊₁ = 2(f₂) - 1 = 2(5) - 1 = 10 - 1 = 9

Option B is incorrect
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f₄ = f₃₊₁ = 2(f₃) - 1 = 2(9) - 1 = 18 - 1 = 17

Option C is incorrect
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f₅ = f₄₊₁ = 2(17) - 1 = 34 - 1 = 33

Option D is correct
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f₆ = f₅₊₁ = 2(33) - 1 = 66 - 1 = 65

Option E is incorrect
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Two correct answers are A and D

A sequence is defined recursively by the following rules:\[ f(1)=3 \]\[ f(n+1)=2 \cdot f(n)-1 \]Which of the following statements are true about the sequence? Select TWO that apply.A. \( f(2)=5 \)B. \( f(3)=10 \)C. \( f(4)=18 \)D. \( f(5)=33 \)E. \( f(6)=66 \)

Answer :

Other Questions

A sequence is defined recursively by the following rules:

\[ f(1)=3 \]
\[ f(n+1)=2 \cdot f(n)-1 \]

Which of the following statements are true about the sequence? Select TWO that apply.

A. \( f(2)=5 \)
B. \( f(3)=10 \)
C. \( f(4)=18 \)
D. \( f(5)=33 \)
E. \( f(6)=66 \)