Pre Calculus 11 - Arithmetic Sequences

Question

Violin lesson fees started at $46 per hour in January, 1990, and gradually increased by $2 .50 every year. How much is the hourly cost in January of 2014? Hint: It’s not a good idea to just apply tn=t1+d(n-1). How much do you pay in January 1991? 1992? Then use the pattern you see.

I can't figure out why in this question it is noted, "It's not a good idea to just apply *formula*", as I have worked out the question by writing out the yearly increase in cost, which comes out to $103.5 dollars in January 2014.

When put in the same equation that is discouraged to use, I get the same answer; $103.5.

What am I doing incorrectly, or have I done the question correctly?

Tn = t1 + (n-1)d

t24 = 46 + (24-1)2.50

t24 = 46 + 57.50

t24 = 103.5 dollars

Answer 1

I believe you are off by 1 year....

At the beginning of 2014, the price will be $106

The reason is you need 24 FULL years, and in the formula you have 23 years

46 + (2014-1990)*2.50 = 46 + 24*2.50 = 106