Question

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....

Answer 1

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

Answer 2

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