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16 July, 12:06

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 ...

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Answers (2)
  1. 16 July, 13:31
    0
    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
  2. 16 July, 13:48
    0
    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
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