Find combinations of Arithmetic Sequence and multiplier, to have a 'X' which stays constant

[seveera]

Hi, I'm tasked to find combinations of different Arithmetic Sequence and multiplier -->>> where the result in column 'E' for 'X' remains constant in all the rows, irrespective of the values of Arithmetic Sequence and multiplier

I'm looking for a formula or steps to calculate/a method, to have a result under column 'X', where all the rows have the same number/result. Appreciate any help/guidance

 

[Dr.Peterson]

Hi, I'm tasked to find combinations of different Arithmetic Sequence and multiplier -->>> where the result in column 'E' for 'X' remains constant in all the rows, irrespective of the values of Arithmetic Sequence and multiplier

I'm looking for a formula or steps to calculate/a method, to have a result under column 'X', where all the rows have the same number/result. Appreciate any help/guidance


View attachment 33387

It isn't clear what you are doing here.

First, column B is not an arithmetic sequence; it's a geometric sequence, where you start with 35 and multiply by 1.2 repeatedly, rounding the display to the nearest integer. Then column C is that sequence multiplied by 5 (and again rounded for display). Column D is the sum of terms of B above that row; and column E is the difference between C and D, that is, between one term of B multiplied by 5 and the sum of terms above it.

There is a formula for the sum of a geometric series, so you could get column C directly, and set that equal to the given multiple of one term.

What is unclear (besides why in the world you want to do this) is what the inputs are, and what you want to set in order to attain the goal. Is it that, given the 1.2 and the 35, you want to choose the 5 to give the constant result? And does column E have to be actually constant, or only when rounded?

 

[seveera]

It isn't clear what you are doing here.

First, column B is not an arithmetic sequence; it's a geometric sequence, where you start with 35 and multiply by 1.2 repeatedly, rounding the display to the nearest integer. Then column C is that sequence multiplied by 5 (and again rounded for display). Column D is the sum of terms of B above that row; and column E is the difference between C and D, that is, between one term of B multiplied by 5 and the sum of terms above it.

There is a formula for the sum of a geometric series, so you could get column C directly, and set that equal to the given multiple of one term.

What is unclear (besides why in the world you want to do this) is what the inputs are, and what you want to set in order to attain the goal. Is it that, given the 1.2 and the 35, you want to choose the 5 to give the constant result? And does column E have to be actually constant, or only when rounded?

Thank you Dr.Peterson, for looking into this..

apologies for not being clear i was working on sales/financial model, the column E represents 'target profit'

What i'm looking for is ->>> (1) if i need to see 100 in column E (this value is the target profit to be achieved, after rounding it to a whole number) from row 1 to 10 ===> then what should be the geometric sequence (column B) and multiplier (column C)...

After the 1st number (ex : 35), every additional row will have a higher number as per a geometric sequence (B) and multiplier (C). B and C are variables, that should change according the value in Column E

35 is just an example, we can start with any number, as far as column E is 100.

The problem statement is : I know the value that i need in column E (that is -> 100). However the geometric sequence (column B) and multiplier (column C) is unknown. Is there a formula that can help to find what the geometric sequence and multiplier value should be used - in order to see the required value (example : 100) in column E

I trying to find the values of column B, C -->>> if i know the value of column E

 

[Dr.Peterson]

Thank you Dr.Peterson, for looking into this..

apologies for not being clear i was working on sales/financial model, the column E represents 'target profit'

What i'm looking for is ->>> (1) if i need to see 100 in column E (this value is the target profit to be achieved, after rounding it to a whole number) from row 1 to 10 ===> then what should be the geometric sequence (column B) and multiplier (column C)...

After the 1st number (ex : 35), every additional row will have a higher number as per a geometric sequence (B) and multiplier (C). B and C are variables, that should change according the value in Column E

35 is just an example, we can start with any number, as far as column E is 100.

The problem statement is : I know the value that i need in column E (that is -> 100). However the geometric sequence (column B) and multiplier (column C) is unknown. Is there a formula that can help to find what the geometric sequence and multiplier value should be used - in order to see the required value (example : 100) in column E

I trying to find the values of column B, C -->>> if i know the value of column E

So, the value for column E is given as the goal (d=175 in the example); all you said before was that it had to be constant, so this is important.

But what else is given, and what can be calculated? In column B, there is a starting number (a=35) and a common ratio (r=1.2). Is either of those fixed? And can the multiplier (m=5) be any number I want?

For example, I can easily work out r and m given a and d. Is that the sort of thing you want? Or should something else be fixed in addition to the difference?

I'll let others deal with the practical issues; for example, since a geometric sequence grows faster and faster (exponentially!), how can you plan on that sort of growth continuing inexorably? I'm ignoring that.