TMUA Official 2021 Paper 2 · Question 10

Official papers

Official 2021 Paper 2 · Q10

Paper 2Logic & proofSequences & seriesNumber & counting

The first seven terms of a sequence of positive integers are:

\begin{aligned} u_1&=15\\u_2&=21\\u_3&=30\\u_4&=37\\u_5&=44\\u_6&=51\\u_7&=59 \end{aligned}

Consider the following statement about this sequence:

$(*)$ If $n$ is a prime number, then $u_n$ is a multiple of 3 or $u_n$ is a multiple of 5.

What is the smallest value of $n$ that provides a counterexample to $(*)$ ?

1

2

3

4

5

6

7

Read the questions freely. Sign in to check your answer, see the worked solution and save your progress.