Hi KP’s,

Please help to solve this question.

Thanks & Regards,

DNLNMUM

Hi KP’s,

Please help to solve this question.

Thanks & Regards,

DNLNMUM

Adwin

a)

Figure Number |
1 |
2 |
3 |
4 |
5 |

No. of triangles |
2 | 3 | 4 | 5 | 6 |

No. of circles |
6 | 8 | 9 | 11 | 12 |

Total no. of shapes |
8 | 11 | 13 | 16 | 18 |

b) Looking at the last row for the total number of shapes, we can see that the pattern is +3, +2, +3, +2… if we group a +3 and a +2 together, we get a +5.

The figure we want to get to is 51 and we already have 8 as a start so we need to find out how many groups of +5 is needed to get there.

First, we take 51 – 8 = 43

43 ÷ 5 = 8 r 3

This means we need 8 groups of +5 or (+2 & +3) and an additional +3 to get to 51.

8 groups of +5 is basically 8 x 2 = 16 patterns

We then add on the first pattern and the last pattern (remainder of +3).

Therefore, the **18 ^{th} pattern** will have 51 shapes.

c) To find the no. of circles, we can take the following steps:

- Add 2 to the quotient of (Figure Number ÷ 2), ignoring any remainder (this is to find the number of rows of circles)
- Multiply the sum by 3 (3 circles per row)
- If the Figure Number is an even number, subtract 1 (as there will be a missing circle at the top right hand corner)

115 ÷ 2 = 57 r 1

57 + 2 = 59

59 x 3 = **177 circles**

DNLNMum

Hi Aswin,

Thank you for the answer.

Regards,

DNLNMUM