Question

(a) if each of them tells 1 person, and then everybody tells exactly 1 other person, and so on, how long will it take until all 450 students in the school hear the rumor? assume that the rate for telling the next person is 1 hour. that is, initially jack and jill know; after 1 hour, 2 more people know; after 2 hours, 2 more people know, . . . .

Answer 1

For this problem I recommend using the explicit version of the arithmetic sequence formula
an = a1 + (n – 1)d.

The first term is a1, the common difference is d, and the number of terms is n. an is the final number we are looking for.


We shall substitute in the common difference and 2 since every hour 2 more people will know. Also the first term is equal to 2. an is 450 because that's what we are looking for.


the equation looks like 450= 2 + (n – 1)2. Now we evaluate. n = 225. 225 terms will pass, then all 450 students will know the rumor. Each term will equal 1 hour . 225 hours converts to 9 full days and 9 hours. So it will take 9 days and 9 hours for every student to know the rumor at that rate.