Each day a runner trains for a 10km race. On the day she runs 1000 m, and then increases the distance by 250m on each subsequent day. On which day does she run a distance of 10km in training? What is the total distance she will have to run in training by the end of that day?

Question

jamesj · Answer

Let s(x) be the distance she runs on day x.
Then 
s(1) = 1000
s(2) = 1250
s(3) = 1500
...

What is the general formula for s(x)?

jamesj · Answer

s(x) = 1000 + .... what?

jamesj · Answer

still there?

4meisu · Answer

Yeah sorry, the one I can find from the textbook is s(x) a1(1-r^n)/1-r

jamesj · Answer

That formula is completely wrong here.

Try and follow the logical path I am leading you on.

jamesj · Answer

s(1) = 1000 + 0
s(2) = 1000 + 250
s(3) = 1000 + 500
s(4) = 1000 + 750
...

See what the formula is now for s(x)?  
s(x) = 1000 + (something involving x)

jamesj · Answer

I'll tell you then.

s(x) = 1000 + 250(x-1)

This is the formula for an arithmetic sequence.  Make sense?

4meisu · Answer

So far, yes.

jamesj · Answer

If so, the way to answer the first question, 

"On which day does she run a distance of 10km in training?"

is to ask for what value of x is

s(x) = 10,000 m ?

jamesj · Answer

So solve now for x.

4meisu · Answer

Okay, thanks!