John Goodman weighs 250 pounds, so he decides to go on a diet. At the end of the first week, he weighs 240. Then at the end of the second week, he weighs 230.

Question

Fill in the blanks of the arithmetic formula [ A(n) = d + a^1(n – 1) ] for this scenario.

A(n) = ___ + _____ (n – 1 ) How much will he weigh at the end of week 12? 140???__

this is what I got so far
250 + ____ (10 - 1)
idk im so confused

Answer 1

since he loses 10 lbs each week, after n weeks he has lost 10n lbs.
So, starting with week 0 (before he started the diet), he weighed 250 lbs,
so, his weight after n weeks on the diet is 250-10n
However, that doesn't quite set up an arithmetic sequence. The nth term is his weight at the beginning of the nth week, or, his weight at the end of the (n-1)st week.

So, if a1 is his starting weight (after zero weeks),
A(n) = 250 - 10(n-1)
But, an AP is written as An = a1 + (n-1)d, so we need to note that the difference each week is -10 from the previous week. That is,
A(n) = 250 + (n-1)(-10)
To check against our first function, note that
250+(n-1)(-10) = 250 -10n+10 = 260-10n
why not 250-10n? Because the AP starts with his starting weight (week 0 of the diet)

Now just plug in your vales for n to find his weight after n weeks.