WHAT WOULD BE THE NEXT NUMBER IN THESE PATTERNS AND WHAT RULE DO THEY FOLLOW?
2,7,6,11,10,
1,2,3,6,7,14,
2 + 5 = 7
7 - 1 = 6
6 + 5 = 11
11 - 1 = 10
What do you think is the next step?
1 * 2 = 2
2 + 1 = 3
3 * 2 = 6
6 + 1 = 7
7 * 2 = 14
What do you think is the next step?
up 5 down 1 up five down 1
up 1 up 1
x2
up 1
x2
x2 ?
To determine the next number in each pattern, let's analyze the sequences and look for a pattern or rule that governs the progression:
1. Pattern: 2,7,6,11,10
Looking closely, we can see that every even term is obtained by subtracting 1 from the previous term, and every odd term is obtained by adding 5 to the previous term.
2 -> 2 + 5 = 7
7 -> 7 - 1 = 6
6 -> 6 + 5 = 11
11 -> 11 - 1 = 10
Based on this pattern, the next number should be obtained by adding 5 to the previous term:
10 + 5 = 15
Therefore, the next number is 15.
2. Pattern: 1,2,3,6,7,14
By observing the sequence, it becomes evident that the pattern doubles each term except for the third number (3), which remains the same.
1 -> Double -> 2
2 -> Double -> 4 (expected)
3 -> Remains same -> 3 (expected)
3 -> Double -> 6 (expected)
6 -> Double -> 12 (expected)
7 -> Double -> 14 (expected)
Based on this pattern, the next number should be obtained by doubling the previous term:
14 * 2 = 28
Therefore, the next number is 28.
To summarize:
Pattern 1: 2, 7, 6, 11, 10, 15 (Add 5 for even terms, subtract 1 for odd terms)
Pattern 2: 1, 2, 3, 6, 7, 14, 28 (Double every term, except 3 which remains the same)