Question

12 term of the AS x-2, 4x, 7x+2

Answer 1

Let x-2, 4x, 7x+2 be three first terms of arithmetical sequence. Then

`a_1=x-2, \\ a_2=4x, \\ a_3=7x+2`.
Since
`d=a_2-a_1=a_3-a_2`, you receive that
`d=4x-(x-2)=7x+2-4x=3x+2`.
The formula for n-th term of arithmetical sequence is:

`a_n=a_1+(n-1)d`.
Hence
`a_(12)=a_1+11d=x-2+11(3x+2)=x-2+33x+22=34x+20`.