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How can I express this sequence/pattern using algebra

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?

Reply 1

mqb2766

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}

Reply 2

RDKGames

Study Forum Helper

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

Reply 3

George Giles

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 😭

Reply 4

George Giles

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.

Reply 5

RDKGames

Study Forum Helper

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.

Reply 6

mqb2766

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.