Example 7 from Algebra and Trigonometry, 13.2 Arithmetic Sequences

Solving Application Problems with Arithmetic Sequences

A five-year old child receives an allowance of $1 each week. His parents promise him an annual increase of $2 per week.

ⓐWrite a formula for the child’s weekly allowance in a given year.
ⓑWhat will the child’s allowance be when he is 16 years old?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. ⓐ
  The situation can be modeled by an arithmetic sequence with an initial term of 1 and a common difference of 2.
  
  Let $A$ be the amount of the allowance and $n$ be the number of years after age 5. Using the altered explicit formula for an arithmetic sequence we get:
  $A_{n} = 1 + 2 n$
2. ⓑ
  We can find the number of years since age 5 by subtracting.
  
  $16 - 5 = 11$
  
  We are looking for the child’s allowance after 11 years. Substitute 11 into the formula to find the child’s allowance at age 16.
  
  $A_{11} = 1 + 2 (11) = 23$
  
  The child’s allowance at age 16 will be $23 per week.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

A woman decides to go for a 10-minute run every day this week and plans to increase the time of her daily run by 4 minutes each week. Write a formula for the time of her run after n weeks. How long will her daily run be 8 weeks from today?

How did it go?

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solution

Your turn

Solution

Your turn