Pre Calculus 11 - Arithmetic Sequences

Question

On Alfredo's 10th birthday, his mother began giving him a weekly allowance of $10 and each week the allowance would increase by $0.50 if he did all his homework. How many weeks would it take for the weekly allowance to become $50 supposing he did all his homework?

I have done out all of the work to this question, and yet while my work is correct, my answer seems to be just a little bit off. Can someone please tell me what I am doing wrong? The correct answer should be 80, and yet I am getting 81.

Tn = t1 + (n-1)d

50 = 10 + (n-1)0.50

50 = 10 + 0.5n - 0.5

50 = 9.5 + 0.5n

40.5 = 0.5n

40.5/0.5 = 0.5/0.5n

and I get 81 equals n

Answer 1

No you pretty much got it right...

the loop counter is off by 1.... you are counting the current week twice, which is worth $10.

Let N be the number of weeks:

50 = 10 + N*0.5

40 = N * 0.5

400 = 5N

N = 80