It takes Lucy 20 minutes to bike to the pool and 3 minutes per lap to swim in the pool. It takes Dan 30 minutes to jog to the pool and 2 minutes per lap to swim in the pool. Write an inequality that will represent how many
laps Lucy must swim in order for her to spend the same number or more minutes exercising than Dan.

, 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

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a

70 years.

step-by-step explanation: