Ben swims 50,000 yards per week in his practices. given this amount of training, he will swim the 100-yard butterfly in 51.5 seconds and place 10th in a big upcoming meet. ben's coach calculates that if ben increases his practice to 60,000 yards per week, his time will decrease to 46.4 seconds and he will place 7th in the meet. if ben practices 70,000 yards per week, his time will be 44.6 seconds and he will win the meet. in terms of ben's time in the big meet, what is his marginal productivity of the number of yards he practices?

answer: add the !

step-by-step explanation: then we will answer

, 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