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

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In summary, the recursive rules for the given sequences are: a) Tn+1 = Tn + 1.5 b) Tn+1 = 0.1Tn c) Tn+1 = Tn + (the sum of the last two numbers in the sequence)
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recoil33
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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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  • #2
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?
 
  • #3
Thank you so much, I really don't know how i missed that!
 

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

What is the recursive rule for the sequence 2, 6, 8, 14, 22, 36?

The recursive rule for this sequence is to add the previous two terms together, starting with 2 and 6. So, the next term would be 2 + 6 = 8, then 6 + 8 = 14, and so on.

How do you find the next term in this sequence?

To find the next term in this sequence, you would add the two previous terms together. For example, to find the 7th term, you would add 22 + 36, which would give you 58 as the next term.

What is the general formula for this sequence?

The general formula for this sequence is f(n) = f(n-1) + f(n-2), where f(n) represents the nth term in the sequence. In this case, f(1) = 2 and f(2) = 6.

Can this recursive rule be applied to other sequences?

Yes, this recursive rule can be applied to other sequences as long as the initial terms and the pattern of adding the previous two terms together remains the same.

What is the significance of this sequence in mathematics and science?

This sequence is called the Lucas sequence and it has many applications in number theory, algebra, and geometry. It also has connections to the famous Fibonacci sequence and the Golden Ratio.

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