if a bacterium covers three milimetes, and every hour it covers 7 more milimeters, how many milimeters will it cover after 24 hours?

Question

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.

Answer 1

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.