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

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The recursive rule for the sequence 2, 6, 8, 14, 22, 36 is defined as Tn+1 = Tn + Tn-1, where Tn represents the nth term of the sequence. The differences between consecutive terms reveal a pattern where each term is the sum of the two preceding terms, starting from the initial values. This method effectively captures the underlying relationship within the sequence, allowing for the generation of subsequent terms.

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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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