Answer :
The formula for the arithmetic sequence of hours from 1 P.M. to midnight is: aₙ = 13 + (n - 2) * 1
Arithmetic sequence for the positive whole numbers less than 100:
To find the formula for an arithmetic sequence, we need to determine the common difference (d) between consecutive terms.
In this case, the first term (a₁) is 1, and the last term (aₙ) is the largest positive whole number less than 100, which is 99. Since the common difference between consecutive terms is 1, we can use the formula:
aₙ = a₁ + (n - 1) * d
Substituting the values:
99 = 1 + (n - 1) * 1
Simplifying the equation:
n - 1 = 99 - 1
n - 1 = 98
Adding 1 to both sides:
n = 99
Therefore, the formula for the arithmetic sequence of positive whole numbers less than 100 is:
aₙ = 1 + (n - 1) * 1
Arithmetic sequence for the hours of the day from 1 P.M. to midnight:
In this case, the first term (a₁) is 1 P.M., which is equivalent to 13 hours. The last term (aₙ) is midnight, which is equivalent to 12 hours. The common difference (d) between consecutive terms is 1 hour.
Using the same formula as above, we can write:
aₙ = a₁ + (n - 1) * d
Substituting the values:
12 = 13 + (n - 1) * 1
Simplifying the equation:
n - 1 = 12 - 13
n - 1 = -1
Adding 1 to both sides:
n = 0
However, since we're looking for the hours from 1 P.M. to midnight, we want to exclude 1 A.M., which would be n = 0. Therefore, we need to adjust the formula slightly:
aₙ = a₁ + (n - 2) * d
So, the formula for the arithmetic sequence of hours from 1 P.M. to midnight is:
aₙ = 13 + (n - 2) * 1
For more such question on arithmetic sequence visit:
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