How can I express this sequence/pattern using algebraWatch
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 will involve . 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.
Now you can try and use this to determine since you know at least two terms.
Thanks for your help, it seems that this level of math is somewhat beyond me at the moment, cannot make sense of your equation 😭
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.
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