9. 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.
Fill in the blanks of the arithmetic formula [ A(n) = d + a1(n – 1) ] for this scenario.
A(n) = _____ + _____ (10– 1 )
How much will he weigh at the end of week 12? ___
Actually, the usual formula is written as
A(n) = a1 + (n – 1)d
You know a1)250) and d(-10), so plug them in and set n=12
In this scenario, we can use the given information to solve for the values in the arithmetic formula. Let's break it down step by step:
1. Identify the given information:
- The initial weight: a1 = 250 pounds
- The difference in weight between weeks: d = -10 pounds (as John loses 10 pounds each week)
2. Plug the values into the formula to find A(n) for the first week:
A(1) = d + a1(1 - 1)
A(1) = -10 + 250(1 - 1)
A(1) = -10 + 250(0)
A(1) = -10 + 0
A(1) = -10
Therefore, John weighs 240 pounds at the end of week 1.
3. Plug the values into the formula to find A(n) for the second week:
A(2) = d + a1(2 - 1)
A(2) = -10 + 250(2 - 1)
A(2) = -10 + 250(1)
A(2) = -10 + 250
A(2) = 240
Therefore, John weighs 230 pounds at the end of week 2.
4. Apply the arithmetic formula to find A(n) for week 12.
A(n) = d + a1(n - 1)
A(12) = -10 + 250(12 - 1)
A(12) = -10 + 250(11)
A(12) = -10 + 2750
A(12) = 2740
Therefore, at the end of week 12, John will weigh 2740 pounds.