Foundation January 2020 Paper 2R Q9

EdexcelCurrent spec6 marksSequences

9 Here is a sequence of patterns made from circles.

Pattern number 1: 1 circle. Pattern number 2: a centre circle with one circle up-left, one down-left and one to the right (4 circles). Pattern number 3: each of the three arms has 2 circles (7 circles). Pattern number 4: each arm has 3 circles (10 circles)
(a) In the space below, draw Pattern number 5 (1)
(b) Complete the table.
Pattern number123456
Number of circles14710
(1)
(c) Work out the number of circles in Pattern number 8 (1)

\(C\) is the number of circles in Pattern number \(P\)

(d) Write down a formula for \(C\) in terms of \(P\) (2)

A different sequence of patterns is made from triangles.
The rule to find the number of triangles in each pattern is

multiply the Pattern number by 5 and subtract 4
(e) Is there a pattern in this sequence that is made from exactly 136 triangles?
You must give a reason for your answer. (1)
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