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arithmetic sequence?
You decided to save some money from January 1st, 2016. You started with a dollar a day, but have been increasing by 1 dollar each day. That is on 1/1/2016, you saved 1 dollar. On 2/1/2016, you saved 2 dollars. On 3/1/2016, you saved 3 dollars. On 4/1/2016, you saved 4 dollars and so on. How much money will you have saved by the 31/12/2016 if you keep saving in this manner? (assume 365 day calendar). I FIGURED THE ANSWER AS 66975$
Following from question , how many years will it take to save 1,000,000 dollars? Hint: When you see lots of digits in these kind of problems, always useful if you re-write it as〖 10〗^6, rather than using 1,000,000.
^^ why do we use quadratic formula
1 Answer
- 5 years ago
S = (365/2) * (1 + 365)
S = (365/2) * 366
S = 365 * 183
S = 66795
Do you continue with the increase or do you go back to 1 dollar on New Year's Day, 2 dollars the next day, etc...
1000000 / 66795 = 14.9711804776 (if you reset at the beginning of the year)
Or
1000000 = (n/2) * (1 + n)
2000000 = n * (n + 1)
2000000 = n^2 + n
0 = n^2 + n - 2000000
n = (-1 +/- sqrt(1 + 8000000)) / 2
n = (-1 +/- sqrt(8000001)) / 2
3.87318808428 years (if you keep increasing your savings by a dollar per day)
