Can you predict the number of squares in Stages 5 and 6 of the sequence ? In Stages 10, 11 and 12 Class 9
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Can you predict the number of squares in Stages 5 and 6 of the sequence ? In Stages 10, 11 and 12 Class 9
Question 1.
Can you predict the number of squares in Stages 5 and 6 of the sequence ? In Stages 10, 11 and 12 ? In Stage 20 ? At any stage? Class 9
Answer:
The number of squares at successive stages is 1, 5, 9, 13, ...
At each stage, 4 squares are added.
So, the number of squares at successive stages can be written as
| Stage (n) | Numbers of Squares |
| 1 | 1 |
| 2 | 1 + 4 = 5 |
| 3 | 1 + 4 + 4 = 9 |
| 4 | 1 + 4 + 4 + 4 = 13 |
| … | … |
| n | 1 + (n – 1) × 4 |
∴ At stage n, number of squares
= 1 + (n - 1) × 4 = 1 + 4n - 4 = 4n - 3
By using this formula,
Stage 5 = 4(5) - 3 = 17
Stage 6 = 4(6) - 3 = 21
Stage 10 = 4(10) - 3 = 37
Stage 11 =4(11) - 3 = 41
Stage 12 = 4(12) - 3 = 45
Stage 20 = 4(20) - 3 = 77
∴ At any stage n, the number of squares is given by 4n - 3.