SOLUTION: The third term of an AP is ten more than the first term while the fifth term is 15 more than the second term. find the sum of the 8th and 15th term of the Ap if the 7th term is 7 t

We use the formula for the nth term:

an = a1 + (n-1)d

a1 + 2d = a1 + 10
     2d = 10
      d = 5     

a7 = a1 + (7-1)(5) = a1 + (6)(5) =  a1 + 30

a7 = 7a1 

So we have the system of equations:

a7 = 7a1
a7 = a1 + 30

7a1 = a1 + 30
6a1 = 30
a1 = 5

That makes things very easy.  We don't need the formula anymore,
for now we can find any term easily.  That's because the 
arithmetic sequence is just counting by fives:

5,10,15,20,25,30,...

So to find the nth term you just multiply n by 5.

8(5) + 15(5) = 40 + 75 = 115

Edwin