Question
if a bacterium covers three milimetes, and every hour it covers 7 more milimeters, how many milimeters will it cover after 24 hours?
Note: each number must be multiplied by seven. For example, hour 1 there will be 3 millimeters covered. Hour 2, 21 millimeters, hour 3, 147 millimeters will be covered and so on so forth.
Note: each number must be multiplied by seven. For example, hour 1 there will be 3 millimeters covered. Hour 2, 21 millimeters, hour 3, 147 millimeters will be covered and so on so forth.
Answers
GPT 3.5
To find out how many millimeters the bacterium will cover after 24 hours, we can use the formula:
3 + 3x7 + 3x7^2 + 3x7^3 + ... + 3x7^23.
This is a geometric progression with the first term (a) as 3 and the common ratio (r) as 7. The number of terms (n) is 24.
Using the formula for the sum of a geometric progression:
S = a(1 - r^n) / (1 - r),
we can substitute the values and calculate:
S = 3(1 - 7^24) / (1 - 7),
S = 3(-7^24 + 1) / (-6),
S ≈ 145,066,563,576,702,353 millimeters.
Therefore, after 24 hours, the bacterium will cover approximately 145,066,563,576,702,353 millimeters.
3 + 3x7 + 3x7^2 + 3x7^3 + ... + 3x7^23.
This is a geometric progression with the first term (a) as 3 and the common ratio (r) as 7. The number of terms (n) is 24.
Using the formula for the sum of a geometric progression:
S = a(1 - r^n) / (1 - r),
we can substitute the values and calculate:
S = 3(1 - 7^24) / (1 - 7),
S = 3(-7^24 + 1) / (-6),
S ≈ 145,066,563,576,702,353 millimeters.
Therefore, after 24 hours, the bacterium will cover approximately 145,066,563,576,702,353 millimeters.