Two taps drip together at exactly 1: 00pm. one tap then drips again every 68 sec while the other tap continues to drip every 72 sec. at what time will the two taps both drip together again?

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

1. supplementary angles

2. acd and bcd

step-by-step explanation: