Solving C: Recursive Rule for Sequence 2, 6, 8, 14, 22, 36

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The discussion focuses on finding a recursive rule for the sequence 2, 6, 8, 14, 22, 36. Participants note that the differences between terms are 4, 2, 6, 8, and 14, with the observation that after the initial difference, subsequent differences match the sequence values. The key insight is that each term can be derived from the sum of the two preceding terms. This leads to the conclusion that the recursive rule can be expressed as Tn = Tn-1 + Tn-2 for n > 2, with initial conditions provided. The conversation emphasizes the importance of recognizing patterns in sequences to derive recursive formulas effectively.
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Write a recursive rule for each of the following sequences:
(a) 41, 42.5, 44, 45.5, 47, 48.5, 50, …

(b) 300, 30, 3, 0.3, 0.03, 0.003, …

(c) 2, 6, 8, 14, 22, 36, …

-----------------
a) Tn+1 = Tn + 1.5
b) Tn+1 = 0.1Tn
c) ?

For C, The difference is 4, 2, 6, 8, 14,
I've figured out several terms, but they will only solve individual bits of the recursive term.
Someone please explain how i would go upon figuring out the recursive rule for question c?
 
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Do you notice that after the first "4", the differences are the same as the numbedrs in the sequence? What is the sum of two consecutive numbers in the sequence? What is 2+ 6? What is 6+ 8? What is 8+ 14? What is 14+ 22?
 
Thank you so much, I really don't know how i missed that!
 

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