AP 1st term=x+1, 2nd term=2x-1, 4th term=2x+5, find x, a, d

Question

AP 1st term=x+1, 2nd term=2x-1, 4th term=2x+5, find x, a, d

 

Please help me how to find even one of these values. I don't even have the sum of given terms, so I really have no value to progress. 

Answer 1

Hi Xenia,

1st term,   a = x+1, n=1,  

2nd term, a₂ = 2x-1, n =2

4th term   a₄ =2x+5, n =4

For arithmatic series

a_n = a + (n-1)d ,

put n = 2

a₂ = a + (2 - 1)d

2x -1 = x+1 +d

 x - 2 = d   -------------(1)

put n = 4

a₄ = a + (4 - 1)d,  plug in d from(1) and a₄

2x + 5 = x + 1 + 3(x-2)

2x + 5 = x +1 + 3x - 6

2x + 5 = 4x - 5

      10 = 2x

        5 = x

x = 5

a = x +1 = 5 +1 = 6

d = x - 2 = 5 - 3 = 2