1. 1
   A designer arranges square tiles into a growing pattern. Pattern 1 uses 4 tiles, Pattern 2 uses 7 tiles, Pattern 3 uses 10 tiles, and the pattern continues by adding 3 tiles each time.

   (a)

   Which expression gives the number of tiles, $T$, in Pattern number $n$?

   [1 mark]

   • A$T = 3n + 1$
   • B$T = 3n - 1$
   • C$T = 4n$
   • D$T = n + 3$

   (b)

   Using $T = 3n + 1$, how many tiles are used in Pattern 10?

   [1 mark]

   • A28
   • B30
   • C31
   • D34

   (c)

   Which pattern number is the first to use more than 100 tiles?

   [1 mark]

   • APattern 32
   • BPattern 33
   • CPattern 34
   • DPattern 35

   Total for question 1: 3 marks

2. 2
   Deposits into a savings jar follow a pattern: Week 1, £2; Week 2, £6; Week 3, £12; Week 4, £20; and the amount continues to grow as a quadratic sequence.

   (a)

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

   [2 marks]

   (b)

   Using the $n$th term $n^2 + n$ from part (a), calculate how much money is deposited in Week 10.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A charity fundraiser records the number of new donors each month, following a Fibonacci-type rule: Month 1 has 3 new donors, Month 2 has 5 new donors, and each following month's total equals the sum of the two previous months.

   (a)

   Find the number of new donors in Month 3, Month 4 and Month 5, showing your working.

   [3 marks]

   (b)

   The fundraiser claims that the number of new donors in Month 6 will be exactly double the number in Month 4.
   
   Show that this claim is incorrect.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A biologist records a bacteria count that doubles each hour: 5, 10, 20, 40, ... forming a geometric sequence with first term 5 and common ratio 2.

   (a)

   Find an expression for the $n$th term of this sequence, and use it to calculate the 8th term.

   [4 marks]

   (b)

   Determine which term of the sequence $a_n = 5 \times 2^{n-1}$ is the first to exceed 5000.

   [4 marks]

   (c)

   A second bacteria population starts at 3 and triples every hour, forming a geometric sequence with first term 3 and common ratio 3.
   
   Find the smallest term number $n$ for which this second population exceeds 5120 (the 11th term value of the first population found in part (b)).

   [5 marks]

   Total for question 4: 13 marks

End of questions