Question 1 |

The Lucas sequence L_n is defined by the recurrence relation:

L_n=L_{n-1}+L_{n-2}, \; for \; n\geq 3,

with L_1=1 \; and \; L_2=3

Which one of the options given is TRUE?

L_n=L_{n-1}+L_{n-2}, \; for \; n\geq 3,

with L_1=1 \; and \; L_2=3

Which one of the options given is TRUE?

L_n=\left ( \frac{1+\sqrt{5}}{2} \right )^n+\left ( \frac{1-\sqrt{5}}{2} \right )^n | |

L_n=\left ( \frac{1+\sqrt{5}}{2} \right )^n - \left ( \frac{1-\sqrt{5}}{3} \right )^n | |

L_n=\left ( \frac{1+\sqrt{5}}{2} \right )^n+\left ( \frac{1-\sqrt{5}}{3} \right )^n | |

L_n=\left ( \frac{1+\sqrt{5}}{2} \right )^n- \left ( \frac{1-\sqrt{5}}{2} \right )^n |

Question 1 Explanation:

Question 2 |

Consider the following recurrence:

\begin{aligned} f(1)&=1; \\ f(2n)&=2f(n)-1, & \text{for }n \geq 1; \\ f(2n+1)&=2f(n)+1, & \text{for }n \geq 1. \end{aligned}

Then, which of the following statements is/are TRUE?

\begin{aligned} f(1)&=1; \\ f(2n)&=2f(n)-1, & \text{for }n \geq 1; \\ f(2n+1)&=2f(n)+1, & \text{for }n \geq 1. \end{aligned}

Then, which of the following statements is/are TRUE?

**MSQ**f(2^n-1)=2^n-1 | |

f(2^n)=1 | |

f(5 \dot 2^n)=2^{n+1}+1 | |

f(2^n+1)=2^n+1 |

Question 2 Explanation:

Question 3 |

Consider the recurrence relation a_{1}=8, a_{n}=6n^{2}+2n+a_{n-1}. Let a_{99}= K \times 10^{4}. The value of K is .

198 | |

148 | |

226 | |

312 |

Question 3 Explanation:

Question 4 |

Let a_{n} be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of the following is the recurrence relation for a_{n}?

a_{n}=a_{n-1}+2a_{n-2} | |

a_{n}=a_{n-1}+a_{n-2} | |

a_{n}=2a_{n-1}+a_{n-2} | |

a_{n}=2a_{n-1}+2a_{n-2} |

Question 4 Explanation:

Question 5 |

Let a_{n} represent the number of bit strings of length n containing two consecutive 1s. What is the recurrence relation for a_{n}?

a_{n-2}+a_{n-1}+2^{n-2} | |

a_{n-2}+2a_{n-1}+2^{n-2} | |

2a_{n-2}+a_{n-1}+2^{n-2} | |

2a_{n-2}+2a_{n-1}+2^{n-2} |

Question 5 Explanation:

There are 5 questions to complete.

Question 5 all the options are wrongly typed please correct it.

Question 5 all the options are wrongly typed please correct it.

Can you please share more details.

Options Updated.

In the first Question, Ln-2 should be there instead of Ln+2