The sum of two consecutive terms in the arithmetic sequence 4, 9, 14, 19,... is 503; find these two terms.
the first consecutive term of the arithmetic sequence is __?
the second __?

Question

darkknight · Answer

first you would like to find the eqn for the arithmetic sequence. 
As a hint plus 5 every term. Afterwards you want to find the 2 terms that add to 503

darkknight · Answer

so lets write the eqn out
plus 4 every term
so we have a formula
$$F = a +(n-1)d$$
the sequence starts out with 4, so when 1 = 1 then F = 4
So we know that a = 4

darkknight · Answer

continuing from here,
we need to find d
when n = 2, F =9
So 9 = 4 + (2-1)(d)
9 = 4 + d
d = 5

darkknight · Answer

now lets test if this eqn works 
$$F= 4+(n-1)5$$

darkknight · Answer

plug in 3 for n and see if you get 14