Math mini-contest problem for Day 24 on D.Buzz for February 2021 π
Math problem for Day 24 π
Turner decided to power up a lot of Hive Power (HP) by vesting 500 HP on the first Monday, 510 HP on the second Monday, 520 HP on the third Monday, and so on. On which Monday would he have already vested at least 100,000 HP without HP inflation?
0
0
0.000
My guess this time is the 101st Monday after the start of this pattern. My work is in the following comment.
This is a sigma question and basically every Monday is calculated by 500 + 10(x-1) where x is the week.
I was a bit lazy so I used a sigma calculator this time around and at x=101, you now had a number greater than 100,000.
Work-wise I put done how I would do it.
Sigma(490)+Sigma(10x) = 100,000 then solve for x but I am a bit lazy.
He'll have 100,000 HP on the 197th monday.
I think the equation goes overtime because the HP accumulates. Day 2 by your formula would be 1020, but instead it should be 1030. Day 3 1530 not 1560.
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Actually I am wrong! The first week, n is zero not one!
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Just noticed that formula is wrong in another aspect...
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π
101st Monday.
I brute forced using the formula
(500*n)+((((n-1)/2)*(1+(n-1)))*10) > 100000
. This incorporates Gauss' formula for the sum of sequential numbers.Posted via D.Buzz
Answer for Day 24 Math Problem
The problem is in arithmetic series under algebra. It requires a bit of "trial and error" (or better said as "guess and check"), since we don't have the nth term of the series.
The formula for the sum of arithmetic series is the following:
where
We also need the nth term of the series. The formula for the nth term of an arithmetic sequence is the following:
where
We know that if the common difference is 0, n is exactly 200. Therefore, we can start making guesses by dividing n by 2, which gives us n = 100.
First, we need to get the value of the nth term. The common difference of the arithmetic series is 10, which is obtained by getting the difference between any two consecutive terms in the series.
an = a1 + (n - 1) * d
an = 500 + (100 - 1) * 10
an = 1490
By testing n = 100, we get the following:
S = 100 * (500 + 1490) / 2
S = 99500
99,500 is very close to 100,000. If we add the 101st term which is 1,500, the cumulative amount is 101,000. We now have an answer.
In the original problem, Turner would have vested at least 100,000 Hive Power on the 101st Monday.
Winner: @jfang003 π
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