This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Here are the solutions to the patterns:
Sam is creating patterns with numbers and shapes. a) The pattern increases by 2 each time. b) The pattern decreases by 10 each time. c) The pattern increases by 5 each time. d) The pattern increases by 1 each time.
What are the next five shapes in this pattern? The pattern is Circle, Square, Triangle, and it repeats. The given shapes are Circle, Square, Triangle, Circle. The next five shapes are:
Colour circle pattern a) Which colour circle comes next in this pattern? The pattern of shades is Light Grey, Medium Grey, Dark Grey, Light Grey. This suggests a repeating pattern of three shades. The next circle in the pattern would be the Medium Grey circle.
b) There are now nine circles in Sam's pattern. How many are green? Assuming the pattern of shades (Light Grey, Medium Grey, Dark Grey) repeats, and one of these shades represents "green". If the pattern repeats for 9 circles, each shade will appear times. Therefore, there are green circles (assuming "green" corresponds to one of the repeating shades).
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1. Sam is creating patterns with numbers and shapes.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.