Afamily of five is taking an extended vacation. every day at lunch they stand in line at a cafeteria in a different order than ever before. on the last day, however, they can't repeating a previous order. their vacation lasted

Their vacation lasted 121 days.

Step-by-step explanation:

Consider the provided information.

A family of five is taking an extended vacation. Every day at lunch they stand in line at a cafeteria in a different order than ever before.

Therefore, the number of possible ways are:

On the last day, however, they can't help repeating a previous order.

That means on the last day they repeat the previous order.

Therefore the total number of ways are:

Hence, their vacation lasted 121 days.

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5