58
Sequences
Q5
Q6
Q7
In the following sequences, write down the next 3 terms and the nth term:
a) 7, 10, 13, 16,... b) 12, 17, 22, 27,...
c) 6, 16, 26, 36,... d) 54, 61, 68, 75,...
\ / \ / \ / "\ /- / \
The pattern above is based on individual triangles. a) Write down the number of individual triangles in each group shown above. b) Work out the number of individual triangles that would be in each of the next three groups. c) Find a formula for the number of individual triangles in the nth term of the pattern.
\ \ 1 1 \ \ I I I I 1 / / / / / For the increasing/decreasing difference _ type questions, you've got to work out how much the difference changes each time. z/ // \\N
Write down the next three terms and nth term of:
a) 5, b) 6, c) 9, 8, 12, 17,... 9, 14, 21,... 12, 19, 30,... e) 729, 243, 81, f) 31250, 6250, g) 12288, 3072, 27,... 1250, 250,... 768, 192,...
Q8
d) 14, 19, 27, 38,...
h) 5103, 1701, 567, 189,...
Hannah is tiling her kitchen floor. She's making a square pattern with grey and white tiles. In the centre there will be a grey tile. The rest of the pattern will be made up of alternating grey and white tiles, with the four corner tiles of the square being grey. Assume that n = 1 in the pattern shown opposite.
Work out, in terms of n, the formula for: a) the number of grey tiles Hannah will need to buy b) the number of white tiles she will need to buy c) the total number of tiles needed.
SECTION FOUR - SEQUENCES, FUNCTIONS AND GRAPHS