How many days would it take to get $1,000,000. Explain!

1 penny on Day 1

2 pennies on Day 2

3 pennies pn Day 3

And so on ...

It's an arithmetic sequence

an = n

the sum of an arethmatic sequence =

n * (an+a1) / 2

substitute an with n and a1 with 1, the sum is 1000

n * (n+1) / 2=1000

n * (n+1) = 2000

n^2 + n - 2000 = 0

solve it with the quadratic formula.

n = 44.22 days

It's an arithmetic progression with a=1 & d=1

Last term in a AP=a + (n-1) d (n=the number of days)

& the sum of a AP = (1st term (a) + last term) n/2

Replace in the sum, last term by its value

SUM = [a + (a + (n-1) d]n/2

1,000,000=[1+1+n-1]n/2

1,000,000 = (n+1) (n/2)

2,000,000 = n²+n===>n²+n-2,000,000=0

Solve this quadratic equation to find the number of days that is n

You will find n=1,413.7 days ≈1414 days