Number sequences and patternsIB MYP Maths Extended: Subtopic test

1. 1
   A sequence begins $7,\ 11,\ 15,\ 19,\ \ldots$ and continues in the same way.

   (a)

   Which expression gives the $n$th term of the sequence?

   [1 mark]

   • A$4n+3$
   • B$3n+4$
   • C$4n-3$
   • D$7n$

   (b)

   Find the $50$th term of the sequence.

   [1 mark]

   • A$200$
   • B$207$
   • C$203$
   • D$199$

   (c)

   Show that $150$ is not a term in the sequence.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The first five triangular numbers are $1,\ 3,\ 6,\ 10,\ 15$.

   (a)

   Find the next two triangular numbers.

   [1 mark]

   • A$20,\ 25$
   • B$21,\ 28$
   • C$21,\ 27$
   • D$22,\ 30$

   (b)

   Which of these numbers is a triangular number?

   [1 mark]

   • A$20$
   • B$25$
   • C$32$
   • D$36$

   (c)

   Find the $10$th triangular number.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The first three terms of a sequence are $20,\ 17,\ 14$, and the sequence continues with the same common difference.

   (a)

   Find an expression for the $n$th term of the sequence.

   [3 marks]

   (b)

   (i) Find the first term of the sequence that is negative.
   (ii) Determine whether $-40$ is a term of the sequence.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A café pushes square tables together edge to edge in a single row. One table seats $4$ people, two joined tables seat $6$ people and three joined tables seat $8$ people. One person sits at each free edge of a table.

   (a)

   (i) Find the number of people seated by four joined tables and by five joined tables.
   (ii) Find the $n$th term for the number of people seated by $n$ tables, and explain it by referring to the way the tables are arranged.
   (iii) Verify your rule for six tables by counting the free edges.

   [6 marks]

   (b)

   A group of $31$ people books the café.
   (i) Find the smallest number of tables needed to seat the group in a single row.
   (ii) The room is only wide enough for $12$ tables in a row. The owner uses two separate rows with the same number of tables in each row. Find the smallest total number of tables needed and justify that this arrangement seats the group.
   (iii) State one assumption made by the model.

   [6 marks]

   Total for question 4: 12 marks

End of questions