2,1,6,14,40

The sequence follows a pattern where each term is twice the sum of the two preceding terms.

Step-by-Step Explanation:

1. Given Sequence: 2, 1, 6, 14, 40

2. Identify the Pattern:

3. Recurrence Relation:

( a(n) = 2

imes (a(n-1) + a(n-2)) )

4. Next Term Calculation:

( a(6) = 2

imes (40 + 14) = 2

imes 54 = 108 )

Answer: The next term in the sequence is 108.