Related Skills

► Pattern Sums

1) Study the number pattern below.

(a) What is the sum of the two numbers in Row 100?

(b) What are the two numbers in Row 100?

(c) Under which column, A,B,C or D, will have 587 appear?

Ans :- a) 399

b) 199 and 200

c) Under column B.

2) Sam forms a pattern using his Lego blocks as given in the figures below.

Figure |
Number of Black Lego Blocks |
Number of White Lego Blocks |
Total number of Lego Blocks |

1 | 1 | 0 | 1 |

2 | 3 | 1 | 4 |

3 | 6 | 3 | 9 |

4 | ? | 6 | 16 |

(a) Complete the table above for Figure 4.

(b) How many White Lego blocks would Figure 16 have

(c) Which would require a total of 784 blocks?

Ans :- a) 10

b) 120

c) 28

3) The following figures are made up of small squares and dots. Look at the figures below and answer the following questions.

Figure number |
Number of small squares |
Number of dots. |

1 | 1 | 4 |

2 | 4 | 9 |

3 | 9 | 16 |

(a) Calculate the number of small squares for figure 4.

(b) Calculate the number of dots for figure 10.

(c) Which figure contains 256 dots?

Ans :- (a) There are 16 small aquares.

(b) There are 121 dots.

(c) Figure 15 contains 256 dots.

4) Observe the patterns carefully.

(a) How many dots are there in Pattern 5?

(b) Which pattern in the series has 1052 dots?

Ans :- a) 17 dots in Pattern 5

b) Pattern 350

5) Study the pattern below.

1 | 1 + 1 |

2 | 1 + 2 + 2 + 1 |

3 | 1 + 2 + 3 + 3 + 2 + 1 |

4 | 1 + 2 + 3 + 4 + 4 + 3 + 2 + 1 |

5 | 1 + ? + ? + ? + ? + ? + ? + ? + ? + 1 |

(a) Complete the pattern of the fifth line by writing your answers in the brackets provided.

(b) What is the sum of the numbers in the 5^{th} line?

(c) What is the sum of the numbers in the 50^{th} line?

Ans :- a) 2,3,4,5,5,4,3,2.

b) 30

c) 2550

6) A number sequence is shown below.

3, 7, 3, 5, 2, 3, 7, 3, 5, 2, 3, 7, 3, 5, 2...

(a) what is the sum of the first 99 numbers?

(b) what is the 128^{th} number?

Ans :- a) 398

b) 3.

7) Dots are drawn at regular intervals along the sides of a hexagon.

(a) If 138 dots are drawn, how many dots are there on each side?

(b) If there are 96 dots on each side of the hexagon. how many dots are there altogether?

Ans :- a) There are 24 dots on each side

b) Altogethere there are 570 dots.

8) Study the pattern. Each solid is made up of identical sticks.

(a) How many sticks will be needed to form Solid 7?

(b) If there are 428 sticks, how many cubes will there be?

Ans :- a) 60 stickes will be needed

b) 53 cubes .

9) Study the number sequence below carefully:

2, 3, 8, 10, 11, 2, 3, 8, 10, 11, 2, 3, 8, 10, 11, ....

(a) How many '8' are there in the first 72 numbers of the above sequence?

(b) Find the sum of the first 72 numbers in this sequence.

Ans :- a) 14 numbers

b) 481 .

10) Aziz stacked some Lego blocks as shown below. He then continued to stack until he had 10 layers.

(a) Find the number of blocks in the 10th layer.

(b) How many blocks did he use altogether?

Ans :- a) 10 b) 55.