Question

Five girls decide to spread a rumor. Within the first hour, each girl tells four other

Answer 1

Answer:

1705

Step-by-step explanation:

This is a sequence where the first term, a=5

Since each girl tells 4 other people, the number of people told after the first hour =20

Each subsequent hour, each person that knows the rumor  continues to tell four more people about it.

Therefore we have the sequence: 5, 20, 80,...

This is a geometric sequence in which the:

• First term, a=5
• Common ratio, r=4

To determine the number of people, y who have heard the rumor after x hours, we simply find the sum of the geometric sequence.

$\text{Sum of a Geometric series},y=\dfrac{a(r^x-1)}{r-1} \\ After 5 hours, x=5\\y=\dfrac{5(4^5-1)}{4-1} \\y=\dfrac{5(1023)}{3}\\\\y=1705$

Therefore, the total number of people who know about the rumor after five hours is 1705.