How can I express this sequence/pattern using algebra

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George Giles
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Here is the sequence of numbers 1, 7, 19, 43, 91, 187 the increment of increase doubles from it's previous term e.g 6 12 then 24 ... How can I express this using algebra?
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mqb2766
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(Original post by George Giles)
Here is the sequence of numbers 1, 7, 19, 43, 91, 187 the increment of increase doubles from it's previous term e.g 6 12 then 24 ... How can I express this using algebra?
x_{n+1} = x_n + 6*2^{n-1}
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RDKGames
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(Original post by George Giles)
Here is the sequence of numbers 1, 7, 19, 43, 91, 187 the increment of increase doubles from it's previous term e.g 6 12 then 24 ... How can I express this using algebra?
Ok so clearly it doubles so there is going to be a 2 involved. More precisely, a power of 2 because it doubles every time you increase the step, so the expression for u_n will involve 2^n. But that's not enough to match with the sequence. Have a go at finishing the final touches
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George Giles
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(Original post by mqb2766)
x_{n+1} = x_n + 6*2^{n-1}
Thanks for your help, it seems that this level of math is somewhat beyond me at the moment, cannot make sense of your equation 😭
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George Giles
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(Original post by RDKGames)
Ok so clearly it doubles so there is going to be a 2 involved. More precisely, a power of 2 because it doubles every time you increase the step, so the expression for u_n will involve 2^n. But that's not enough to match with the sequence. Have a go at finishing the final touches
Countless hours have led me nowhere... thanks for your help I can see how a power needs to be implemented but cannot get to grips with it as a whole.
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RDKGames
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(Original post by George Giles)
Countless hours have led me nowhere... thanks for your help I can see how a power needs to be implemented but cannot get to grips with it as a whole.
Well an educated guess would be to say that the sequence might in the form u_n = a\cdot 2^n + b.

Now you can try and use this to determine a,b since you know at least two terms.
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mqb2766
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(Original post by George Giles)
Thanks for your help, it seems that this level of math is somewhat beyond me at the moment, cannot make sense of your equation 😭
Next value = previous value + Difference

Difference is 6, 12, 24, 48
The common ratio is r = 2 as 12/6 = 24/12 = 48/24 so it is a geometric sequence and is of the form 2^n.
The initial value is 6
Difference = 6*2^(n-1).
The (n-1) is so that the the initial value n=1 is 6.

Hope that helps. I'm presuming you've done geometric sequences. Also the sum of a geometric sequence is another sequence (or the difference is a sequence), so you could get a position to term as above, not just a term to term.
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SerBronn
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Let's call the sequence x_0 = 1, x_1 = 7, x_2 = 19, .... We want a general formula for x_n.

x_1 - x_0 = 6
x_2 - x_1 = 12
x_3 - x_2 = 24
...
x_{n-1} - x_{n-2} = 6 \times 2^{n-2}
x_n - x_{n-1} = 6 \times 2^{n-1}

Now the clever part ... add up all the equations noting that on the left-hand sides virtually every term cancels out. We are left with

x_n - x_0 = x_n - 1 = 6 \times (1 + 2 + 4 + ... + 2^{n-1}) = 6 \times (2^n - 1)
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