A new fitness center opened up with 24 clients. Each week they are signing up an average of 5 new members. The business owner wrote the explicit formula for this situation as being A(n) = 24 + (n - 1)(5). Is this correct for this situation? Justify your answer using complete sentences and proper grammar.

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A new fitness center opened up with 24 clients. Each week they are signing up an average of 5 new members. The business owner wrote the explicit formula for this situation as being A(n) = 24 + (n - 1)(5). Is this correct for this situation? Justify your answer using complete sentences and proper grammar.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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so i think no .. They start with 24. And get 5 a week. I am assuming the n stands for the week. A=24 + 5(n)  am i right ?
  • phi
it depends on what we count as week 1. Normally people count week 1 as the starting point (where A = 24) so you would want the formula in the question A= 24 + (n-1)*5

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Other answers:

  • phi
Your equation A(n)= 24+5n means you start counting at n=0 we could do that, but (unfortunately) the people who wrote this question assume we start at n=1. They assume that, because that is how sequences are often taught, and they don't expect the student to think too much about it.
but why would n -1 ?
  • phi
you want A(1) to be 24 if you use A(n)= 24+5*n we would get A(1)= 24+5*1 = 29 (i.e. 5 too many) to fix it up, we first subtract 1 from n. now it will work A(1)= 24 A(2)= 29 (5 more) A(3)= 34 , etc
Ohhhhh , thank you !
  • phi
The formula tells you how to figure out how many members there will be, depending on the week. We start with week 1 , with 24 members

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