Please help explain how to work my math problem (finding the formula!) >o< *urgent?! *

I'm suppose to find the forumla for the arithmetic sequence.

a(1)=5 a(4)=15

the numbers in (x) are under the a's so its like a exponnet but under if you can know what im saying? :s

the answer was
a(n) =10/3n+5/3

I have no clue how that worked out so if someone can explain much would be appreicated! :)

The general formula for the nth term of an arithmetic sequence is (as you should know)

a_n = a_1 + (n - 1)d

where d is the common difference. Using the information you were given,

a_4 = 5 + (4-1)d
15 = 5 + 3d
10 = 3d
10/3 = d

so the formula is

a_n = 5 + (n-1)(10/3)
  = 5 + (10/3)(n) - (10/3)
  = (10/3)(n) + (5/3)