What are the next two terms in the pattern ,3,6,5,10,9,18,17?
Not even the very sophisticated Wolfram couldn't find a pattern
www.wolframalpha.com/input/?i=pattern+%7B3%2C6%2C5%2C10%2C9%2C18%2C17%7D
double, subtract 1, double, subtract 1, ...
3,6,5,10,9,18,17,34,33,66,65, ...
To find the next two terms in the pattern, we need to observe the pattern and determine the rule it follows.
Looking at the pattern, we see that each even-indexed term is obtained by doubling the previous term, and each odd-indexed term is obtained by subtracting 1 from the previous term.
Let's examine the terms one by one:
Term 1 (index 0): 3 - Since it is at an odd index, the next term will be obtained by subtracting 1.
Term 2 (index 1): 6 - Since it is at an even index, the next term will be obtained by doubling.
Term 3 (index 2): 5 - Since it is at an odd index, the next term will be obtained by subtracting 1.
Term 4 (index 3): 10 - Since it is at an even index, the next term will be obtained by doubling.
Term 5 (index 4): 9 - Since it is at an odd index, the next term will be obtained by subtracting 1.
Term 6 (index 5): 18 - Since it is at an even index, the next term will be obtained by doubling.
Term 7 (index 6): 17 - Since it is at an odd index, the next term will be obtained by subtracting 1.
Based on this pattern, the next term at index 7 (odd index) will be obtained by subtracting 1 from the previous term, which is 17. So the next term will be 16.
Similarly, the term at index 8 (even index) will be obtained by doubling the previous term, which is 16. So the next term will be 32.
Therefore, the next two terms in the pattern are 16 and 32.
To find the next two terms in the given pattern, let's analyze the sequence:
The sequence seems to be alternating between two patterns. The first pattern is multiplying each number by 2, and the second pattern is subtracting 1 from each number.
Starting with the number 3, let's apply these patterns to find the next two terms:
Pattern 1: Multiply by 2
3 × 2 = 6
6 × 2 = 12
Pattern 2: Subtract 1
6 - 1 = 5
12 - 1 = 11
Therefore, the next two terms in the pattern are 12 and 11.