determined the value of x

Question

the first three terms of an arithmetic sequence are 2x-4,x-3 and 8-2x

Answer 1

An arithmetic sequence is of the form a, a+d, a+2d, ... in other words, a+(n-1)d. The difference between any two consecutive terms is constant, so:

x-3-(2x-4)=8-2x-(x-3),

x-3-2x+4=8-2x-x+3,

1-x=11-3x,

2x=10, x=5.

The series is 2x-4, x-3, 8-2x=6, 2, -2 where a=6 and d=-4 (T_n=6-4(n-1)).