Question 16 of 49beginner🔧 ApplyShort Answer2 marks

Predict the number of squares in the next three stages of the pattern and write the sequence of numbers up to Stage 7 of the pattern.

Correct Answer

The pattern begins with 1, 3, and 5 squares in the first three stages. Observing the constant difference of 2 between consecutive terms, the next three stages (Stages 4, 5, and 6) will have 7, 9, and 11 squares respectively.

Continuing this pattern, Stage 7 will have 13 squares. Therefore, the complete sequence of numbers up to Stage 7 is 1, 3, 5, 7, 9, 11, 13. This sequence represents consecutive odd numbers, which can be generalized by the linear polynomial 2n−12n - 1.

Exercise: Think and Reflect | Q: 1 | (Page 7)
For More Understanding

Explanation

The context provides a table showing the number of square tiles for the first seven stages as 1, 3, 5, 7, 9, 11, 13. The question asks to predict the next three stages after the initial ones and write the sequence up to Stage 7. The pattern increases by a constant difference of 2 each time, which are consecutive odd numbers, and can be represented by the formula 2n - 1.

Solution Steps

  1. Step 1: Identify the initial pattern of squares: 1, 3, 5.

  2. Step 2: Predict the next three stages (4, 5, 6) by adding 2 to the previous term: 5+2=7, 7+2=9, 9+2=11.

  3. Step 3: Calculate Stage 7 by adding 2 to Stage 6: 11+2=13.

  4. Step 4: Write the complete sequence up to Stage 7: 1, 3, 5, 7, 9, 11, 13.

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