in the video game gemetric constructors a number of the shapes have to be arranged into a predefined form , in level 1, you are given 3 min 20s to complete the task, at each level afterward, a fixed number of seconds are removed from the time until, at level 20 , 1 min 45s are given, what would be the total amount of time given if you were to complete the first 20 levels

Question

in the video game gemetric constructors a number of the shapes have to be arranged into a predefined form , in level 1, you are given 3 min 20s to complete the task, at each level afterward, a fixed number of seconds are removed from the time until, at level 20 , 1 min 45s are given, what would be the total amount of time given if you were to complete the first 20 levels

Answer 1

look at it as an arithmetic sequence , where

term(1) = 3 min , 20s or 200 sec
term(20) = 1 min, 45 sec or 105 seconds

a = 200
a + 19d = 105
subtract..
19d = -95
d = -5

so sum(20) = (20/2)[2(200) + 19(-5)] = 3050 seconds
= 50 min, 50 seconds

Answer 2

To find the total amount of time given to complete the first 20 levels in the game Gemetric Constructors, we need to sum up the time given for each level.

In level 1, the time given is 3 minutes and 20 seconds, which can be converted to 200 seconds (3 * 60 + 20 = 200).

At each subsequent level, a fixed number of seconds is removed from the time given. From level 1 to level 20, the time is reduced by (3 minutes and 20 seconds - 1 minute and 45 seconds) = 95 seconds.

To calculate the time given for each level, we can use the following formula:
TimeGiven(level) = TimeGiven(level-1) - 95

Now, let's calculate the time given for each level:

Level 1: 200 seconds
Level 2: 200 - 95 seconds = 105 seconds
Level 3: 105 - 95 seconds = 10 seconds
...
Level 19: (TimeGiven in previous level) - 95 seconds
Level 20: (TimeGiven in previous level) - 95 seconds

To find the total amount of time given, we need to sum up the time for all levels from 1 to 20:

TotalTimeGiven = TimeGiven(1) + TimeGiven(2) + ... + TimeGiven(20)

We can simplify this expression by observing that each level's time given is 95 seconds less than the previous level:

TotalTimeGiven = (TimeGiven(1) - 0) + (TimeGiven(1) - 95) + ... + (TimeGiven(1) - 95 * 19)

TotalTimeGiven = 20 * TimeGiven(1) - (0 + 95 + ... + 95 * 19)

To calculate the sum of 0 + 95 + ... + 95 * 19, we can use the arithmetic series formula:

Sum = (n / 2) * (first_term + last_term)
where n is the number of terms and first_term and last_term are the first and last terms of the series, respectively.

In this case, n = 20 and first_term = 0, last_term = 95 * 19.

Sum = (20 / 2) * (0 + 95 * 19) = 20 * 95 * 19

Now, substituting this value back into our main expression:

TotalTimeGiven = 20 * TimeGiven(1) - (20 * 95 * 19)

Finally, to obtain the total amount of time given to complete the first 20 levels, we need to calculate TimeGiven(1) and substitute it into the formula.

TimeGiven(1) = 3 minutes and 20 seconds = 200 seconds

TotalTimeGiven = 20 * 200 - (20 * 95 * 19)
= 4000 - 36100
= -32100

Therefore, the total amount of time given to complete the first 20 levels in Gemetric Constructors is -32100 seconds.

look at it as an arithmetic sequence , where

Thanks:)

To find the total amount of time given to complete the first 20 levels in the game Gemetric Constructors, we need to sum up the time given for each level.