Question

Some cicadas return every 17 years. Other cicadas return every 13 years. Both kinds appeared together in 2004 in the U.S.a) When was the previous year that theyboth appeared together?b) Predict the next year that they willappear together.

Answer 1

ANSWERS

a)

b)

Step-by-step explanation

Let's say that we have the year 0, where both cicadas were first together at the same time. After 13 years one kind appears and 4 years later (17 years after the first year) the other group appears. Then 26 years after the first year the every-13 years group appeared and 34 years after the first year the every-17-years group appeared. This goes on until both appear together again.

Note that each year each group appears is a multiple of the frequency (13 or 17). Since both numbers are prime - i.e. the