how do we do this, 1st, forget about $.01, lets make it easier to see. lets use $1.

the formula is 2^(n-1)

where n is the number of day. i mean the Day NO.

1st day, 2^(1-1)=2^0=1

2nd day, 2^(2-1)=2^1=2

3rd day, 2^(3-1)=2^2=4

7th day, 2^(7-1)=2^6=64

so 7th day is $64, since you start with a peny, $64/100=$.64 on the 7th day.

now you can find the 20th day.

what happen if you keep tripling everyday? just use 3^(n-1)

so generally, m^(n-1), where m is the number of how many times it increases and n is the day number.

now what happen if you start at $4 and keep doubling? just use 4 x [2^(n-1)], if it keeps tripling, 4 x [3^(n-1)]. its just as simple as that.

now, let me tell you how to find the Sum of all days. lets say

if you start at $1 and keep doubling it for 5 days, find the total money you have in 5 days(not on the 5th day)? how du find that?

ok, if we find how much you have on the 5th day, you use m^(n-1) this formula, so the 5th day is 2^(5-1)=2^4=16

now, how much do you get all 5 days?

1st day you have $1

2nd you have $2

3rd you have $4

4th you have 8

and the 5th day you have 16

all 5 days you have 1+2+4+8+16=$31

how do we do this?

you use m^n-1 this formula, 2^5-1=32-1=31

if you wanna find the total you have in 20 days, 2^20-1=1048576-1=$1048575, if you gain a penny a day, you will get total $10485.75

last word, m^n-1 and m^(n-1) are different just remind you.

to find the total of all days, use m^n-1

to find the total on the specific day, use m^(n-1)

1st term is x

2nd is 2x

3rd is 4x

4th is 8x

5th is 16x

6th is 32x

7th is 64x

and so on.

now consider the numbers in the sequence, 1,2,4,8,16,32,64…

They can be represented as 2^0 [2 to the power of zero],

2^1, 2^2, 2^3, 2^4, 2^5, 2^6…….

So, relating the power of two to the order of the terms,

1st term 0 1st term is 1, or 2^0

2nd term 1 2nd term is 2^1

3rd term 2 3rd term is 2^2

4th term 3

5th term 4

6th term 5

7th term 6

so the nth term will be 2 raised to the power of [n-1]

Was that what you meant ? because if you didn`t, I now feel a

total wally ! ! ! Have a nice day, Twiggy.