Related Skills

► Pattern Sums

1) Jane had 400 beads, she arranged them in rows such that the next row had 2 more beads than the previous row. The diagram shows 4 rows of beads she had arranged. How many rows did she arrange with the 400 beads?

Ans :- 20 rows.

2) Sam started reading a book on Sunday. He read 9 pages on Sunday and continued reading the book for the whole week till Saturday. He increased the number of pages read by 3 pages everyday. He continued the reading pattern until he finished reading the book. How many pages were there in the book?

Ans :- There were 126 pages.

3. The sequence of the figures below is formed by unit squares. Study the patterns carefully and answer questions (a), (b) and (c).

(a) How many unit squares are there in figure 5?

Write your answer in the table below.

Figure |
No. of unit squares |

1 | 3 |

2 | 6 |

3 | 10 |

... | ... |

5 |

(b) Which figure has a total of 36 unit squares?

(c) How many unit squares are there in figure 50?

Ans :- a) 21

b) 7

c) 1326.

4. Observe the following number pattern.

(a) What are the numbers in the boxes?

(b) What is the first number in line 5?

(c) How many numbers are there in line 99?

Ans :- a) 23,25

b) 33

c)197.

5. Study the figures carefully Each figure is made up of sticks, circles and triangles.

(a) How many circles will there be in Figure 38?

(b) In which figure will there be 123 triangles?

(c) How many sticks will be needed to form Figure 150?

Ans :- a) there will be 116 circles

b) It is Figure 62

c) 750
sticks are needed.

6. Given that ∆ + ∆ + ☆ + ☆ = 66 and

□ + □ + ☆ + ∆ = 65

What is the value of □ + ☆ + ∆?

Ans :- 49.

7. Study the pattern carefully and answer the questions that follow. Show your workings clearly in the space provided and write your answers in the blanks.

Pattern Number |
Number of shaded circles |
Number of white circles |
Total number of circles |

1 | 1 | 0 | 1 |

2 | 5 | 4 | 9 |

3 | 9 | 16 | 25 |

4 | 13 | 36 | 49 |

7 | (a) ? | (b) ? | |

12 | (c) ? |

Ans :- a) 25

b) 144

c) 529
.

8.

(a) If Jason adds 1 to the numerator of a fraction, the fraction becomes one whole. If he adds 4 to the denominator, the fraction becomes ½. What is the fraction?

(b) The numbers 1 to 500 are written in columns as shown :

A |
B |
C |
D |
E |

1 | 2 | 3 | 4 | 5 |

9 | 8 | 7 | 6 | |

10 | 11 | 12 | 13 | |

17 | 16 | 15 | 14 | |

18 | 19 | 20 | 21 | |

25 | 24 | 23 | 22 | |

26 | ... | ... | .... |

If this pattern continues, in which column will the number 500 be written?

Ans :- a) ^{5}⁄_{6}

b) D.

9. The sequence of figures below is made up of 2-cm cubes. Study the pattern carefully and answer questions (a), (b) and (c).

(a) How many 2-cm cubes are there in Figure 5?

Write your answer in the table below.

Figure |
No. of 2 cm cubes |
No. of layers of cubes |

1 | 1 | 1 |

2 | 5 | 2 |

3 | 14 | 3 |

4 | 30 | 4 |

5 | 5 |

(b) What is the total volume of the cubes in Figure 3?

(c) Given that a figure has 285 cubes, how many layers of cubes will there be?

Ans :- a) 55

b) 112 cm³

c) 9
.

10) The rhombuses below are formed by using matchsticks. Each rhombus has an equal number of matchsticks on its sides.

(a) Complete the following table.

Pattern |
1 | 2 | 3 | 4 | 5 | ... | ... | ... | 30 |

Number of matchsticks |
4 | 12 | 20 | ? | ? | ? |

(b) Which pattern number will you get if 1004 matchsticks are used?

Ans :- a) 28, 36, 236

b) 1004
.