TMUA Official 2023 Paper 2 · Question 16

A sequence is defined by:

\begin{aligned}u_1&=a\\u_2&=b\\u_{n+2}&=u_n+u_{n+1}\quad\text{for }n\ge1\end{aligned}

where $a$ and $b$ are positive integers. The highest common factor of $a$ and $b$ is 7.

Which of the following statements must be true?

I. $u_{2023}$ is a multiple of 7.
II. If $u_1$ is not a factor of $u_2$ , then $u_1$ is not a factor of $u_n$ for any $n>1$ .
III. The highest common factor of $u_1$ and $u_5$ is 7.

Anone of them

BI only

CII only

DIII only

EI and II only

FI and III only

GII and III only

HI, II and III

examday