Chapter 4.7, Problem 68PPE

To determine

To find the rule that represents the sequence of the days in the year that are Fridays and how many full weeks are in a 365-day year.

Answer to Problem 68PPE

No, $a_n=4+(n-1)7$ , $52$

Explanation of Solution

Given:

The first Friday of a new year is the fourth day of that year.

Calculation:

The total number of days in a week $=7$

First divide $365$ by $7$ , on dividing, the result is obtained as-

  $\frac{365}{7}=52\frac{1}{7}$ ....... (1)

This means there is only one extra day. But it is given that the first Friday of a new year is the fourth day of that year.

Therefore, it can be guaranteed that there will not be Fridays regardless of normal or a leap year.

The rule that represents sequence of the days in the year that are Fridays is given by −

  $a_n=4+(n-1)7$

This means $4th,11th,18th\mathrm{..........}$ will be the Fridays.

From equation (1), it is clear that the year will have $52$ full weeks in a 365-day year.