Arithmetic sequence - finding the term

[dbush]

I am mother who is trying to help my son who is struggling with algebra. I have a problem that I cannot figure out. I think I have just looked at it and thought about too long. Can you help?

The problem is:
200 is the ____th term of 24, 35, 46, 57,...

I know (or at least I think I know) the basic equation is

a_n ⁼ a₁ ^{+ (n - 1)d}

So - a₁ is 24 and d is 9. Do I do anything with 200?

I know the answer is 17 based on my answer sheet, but how??

By the way, my goal is not to do the problem for my son, I just need to work them out so if he has a question I know how to help guide him. Thank you!

 

[pka]

I am mother who is trying to help my son who is struggling with algebra. I have a problem that I cannot figure out. I think I have just looked at it and thought about too long. Can you help?

The problem is:
200 is the ____th term of 24, 35, 46, 57,...

I know (or at least I think I know) the basic equation is

a_n ⁼ a₁ ^{+ (n - 1)d}

So - a₁ is 24 and d is 9. Do I do anything with 200?

I know the answer is 17 based on my answer sheet, but how??

First, \(\displaystyle d=11\) not 9.
Solve \(\displaystyle 24+11(n-1)=200\)

 

[HopeWelch]

The problem is:
200 is the ____th term of 24, 35, 46, 57,...
a_n ⁼ a₁ + (n - 1)d


200 = 24 + (n-1) 11

200 = 24 + 11n -11

200 = 13 + 11n

200-13 = 11n

187 = 11n

n = 17

You do use the 200 and d is 11 because the terms increase by 11 each step.

 

[dbush]

Boy, that makes all the difference

That's what I get for trying to solve algebra problems while I'm answering the phone. I can't tell you how long I've looked at this. Thanks so much for your help and kindness. I'm sure I'll be back another day. I wish I could be a contributor to this board, but as you can see it's probably not a good idea.