mallory emailed a funny cartoon to Ann. she told ann to send it to five friends with instructions for each of them to send it to five other friends. after four cycles of emailing,how many cartoons will have been sent? the answer is 156 but i don't know how to get thy answer, please help!
To calculate the number of cartoons that will have been sent after four cycles of emailing, let's break down the process step by step.
In the beginning, Mallory emailed the cartoon to Ann. So, there is 1 cartoon.
In the first cycle, Ann sends the cartoon to five friends. Now, we have 1 + 5 = 6 cartoons in total.
In the second cycle, each of those five friends sends the cartoon to five other friends. So, each of the original five friends sends it to five more friends, making a total of 5 x 5 = 25 friends. Including Ann, we have 1 (from the first cycle) + 5 (original friends) + 25 (friends of friends) = 31 cartoons.
In the third cycle, each of those 25 friends sends the cartoon to five more friends. So, it will be 25 x 5 = 125 friends receiving the cartoon. Including the previous numbers, we have 1 + 5 + 25 + 125 = 156 cartoons.
In the fourth and final cycle, each of the 125 friends sends the cartoon to another five friends. Thus, we would have 125 x 5 = 625 friends receiving the cartoon. Overall, there will be 1 + 5 + 25 + 125 + 625 = 781 cartoons at this point. However, we only need to find the number after four cycles, so the final answer would be 156.
Therefore, after four cycles of emailing, the total number of cartoons sent would be 156.