Apply the formula  =  for the n-th term of an AP. You will have

 =  +  = 15.   (1)

 =  +  = 35.   (2)

Take the difference (2) - (1). You will have

8d - 3d = 35 - 15  --->  5d = 20  --->  d =  = 4.

Thus we just found the common difference.

Now,  =  =  +  =  +  = 35 + 6*4 = 35 + 24 = 59.

Answer.  = 59.

4th term





 ------- eq (i)



9th term





 ------- eq (ii)



- 20 = - 5d ------ Subtracting eq (ii) from eq (i)

d, or common difference = , or 4

 ------- Substituting 4 for d in eq (i)









 ------- Substituting 15 for n, 3 for , and 4 for d



 

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