Question 19 of 19intermediate🔍 AnalyzeShort Answer2 marks

What are the digital roots of numbers that are 1 more than a multiple of 6? What do you notice?

Correct Answer

Given: Numbers of the form 6k + 1 (1 more than a multiple of 6)

Calculation: For k = 0: 6(0) + 1 = 1 → digital root = 1 For k = 1: 6(1) + 1 = 7 → digital root = 7 For k = 2: 6(2) + 1 = 13 → digital root = 4 For k = 3: 6(3) + 1 = 19 → digital root = 1 For k = 4: 6(4) + 1 = 25 → digital root = 7

Pattern: 1, 7, 4, 1, 7, 4, ...

Answer: The digital roots cycle through 1, 7, 4.

Observation: Adding 6 changes the digital root by subtracting 3 (since 6 ≡ -3 mod 9).

Exercise: Digital Roots | Q: 4 | (Page Page 19)
For More Understanding

Explanation

Numbers that are 1 more than a multiple of 6 are of the form 6k + 1. For k = 0: 1 (digital root 1). For k = 1: 7 (digital root 7). For k = 2: 13 (digital root 4). For k = 3: 19 (digital root 1). For k = 4: 25 (digital root 7). The pattern cycles through 1, 7, 4 because adding 6 changes the digital root by subtracting 3 (since 6 ≡ -3 mod 9).

Solution Steps

  1. Identify numbers of the form 6k + 1 (1 more than a multiple of 6)

  2. Calculate digital roots for k = 0, 1, 2, 3, 4

  3. Observe the pattern: 1, 7, 4, 1, 7, 4, ...

  4. Note that adding 6 changes the digital root by subtracting 3 (since 6 ≡ -3 mod 9)

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