0 1 3 8 22 63 ()

2025-09-01 阅读 2 评论 0

摘要：The next number in the sequence is 185.
Step-by-Step Explanation:
1. Analyze the differences betwe

The next number in the sequence is 185.

0 1 3 8 22 63 ()

Step-by-Step Explanation:

1. Analyze the differences between consecutive terms:

0 = 1

1 = 2

3 = 5

8 = 14

22 = 41

Differences: 1, 2, 5, 14, 41

2. Observe the pattern in the differences:

The differences themselves form a sequence where each term is 3× the previous difference minus 1:

1 → 2: (1

imes 3

1 = 2)

2 → 5: (2

imes 3

1 = 5)

5 → 14: (5

imes 3

1 = 14)

14 → 41: (14

imes 3

1 = 41)

Next difference: (41

imes 3

1 = 122)

3. Extend the original sequence:

Add the next difference to the last term: (63 + 122 = 185).

Alternate Perspective (Recurrence Relation):

Each term after the second is generated by (a(n) = 3a(n-1)

(n-3)):

(a(3) = 3

imes 1

0 = 3)

(a(4) = 3

imes 3

1 = 8)

(a(5) = 3

imes 8

2 = 22)

(a(6) = 3

imes 22

3 = 63)

(a(7) = 3

imes 63

4 = 185).

Answer: 185

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