5 The grid shows the first three diagrams in a sequence. Each diagram is made using sticks. Diagram 1 Diagram 2 Diagram 3 (a) On the grid, draw Diagram 4. Diagram 4 [1] (b) Complete the table. Diagram number 1 2 3 4 5 Number of sticks 5 9 13 [2] (c) (i) Find an expression, in terms of n, for the number of sticks in Diagram n. ................................................. [2] (ii) One of the diagrams has 73 sticks. Work out its Diagram number. Diagram ................................................. [2] © UCLES 2023 0580/33/M/J/23 11 (d) (i) Show that the total number of sticks needed to make the first 3 diagrams is 27. [1] (ii) The total number of sticks needed to make the first k diagrams is 2k2+3k. Show that this expression gives the correct total number of sticks needed to make the first 3 diagrams. [2] (iii) Tobias wants to make the first 10 diagrams. He has already made the first 3 diagrams. He has 240 sticks left to make the remaining 7 diagrams. Work out how many sticks he has left when all 10 diagrams are made. ................................................. [4] © UCLES 2023 0580/33/M/J/23 [Turn over 12