Mr. rr the rreliable rrobot has been programmed to whistle every $18$ seconds and do a jumping jack every $42$ seconds, starting from the moment he is turned on. (for example, he does his first jumping jack $42$ seconds after he is turned on.)

how many times during the first $15$ minutes after activation will mr. rr whistle and do a jumping jack at the same instant?

7 times during the first 15 minutes

Step-by-step explanation:

Remember that

so

Decompose the numbers 18 and 42 in prime factors

we know that

Find the least common multiple (LCM)

The LCM is

we need to find all multiples of 126 that are less than or equal 900.

therefore

7 times during the first 15 minutes

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5