sequence and series

Carol starts a new job on a salary of 20,000. She is given an annual wage rise of £500 at the end of every year until she reaches maximum salary of 25,000. Find the total she earns( assuming no other rises) over 15 years

I was using the formula Sn n/2{2a+(n-1)d}
and i got the answer of 352500 but the answer booklet says that it should be 347500 and i don't understand why?

Does her salary rise every year?

i'm sorry i don't understand what you mean or how to do this question?

You have started well

BUT

If you look at your method you have assumed that her salary goes

20000
20500
21000

etc

for the full 15 years

If that were the case, in the 15th year she would earn 20000 + 14*500 = 27000

BUT

the questions says that she never earns that much

So you need to split your question up into the years where her pay is increasing and the years where she is at maximum salary

I calculated that she will earn £222500 in the first 10 years but i don't know what to do now?

Carol starts a new job on a salary of 20,000. She is given an annual wage rise of £500 at the end of every year until she reaches maximum salary of 25,000. Find the total she earns( assuming no other rises) over 15 years

I was using the formula Sn n/2{2a+(n-1)d}
and i got the answer of 352500 but the answer booklet says that it should be 347500 and i don't understand why?