Respuesta :
To find the rule in the series, let's examine the differences between consecutive terms:
3 - 2 = 1
3 - 3 = 0
5 - 3 = 2
10 - 5 = 5
13 - 10 = 3
The differences between consecutive terms are alternating: 1, 0, 2, 5, 3. This pattern is not immediately clear, so let's examine the second differences:
0 - 1 = -1
2 - 0 = 2
5 - 2 = 3
3 - 5 = -2
The second differences are also alternating: -1, 2, 3, -2.
It appears that the second differences are increasing by 1 each time. This suggests a quadratic pattern.
Let's find the next term using this pattern:
3 + 4 = 7
So, the next term in the series is 7.
Therefore, the series is: 2, 3, 3, 5, 10, 13, 7.
3 - 2 = 1
3 - 3 = 0
5 - 3 = 2
10 - 5 = 5
13 - 10 = 3
The differences between consecutive terms are alternating: 1, 0, 2, 5, 3. This pattern is not immediately clear, so let's examine the second differences:
0 - 1 = -1
2 - 0 = 2
5 - 2 = 3
3 - 5 = -2
The second differences are also alternating: -1, 2, 3, -2.
It appears that the second differences are increasing by 1 each time. This suggests a quadratic pattern.
Let's find the next term using this pattern:
3 + 4 = 7
So, the next term in the series is 7.
Therefore, the series is: 2, 3, 3, 5, 10, 13, 7.
