Question 1015023
.
If (x+1), (-2x+4) and (x+15) are 3 consecutive terms of an arithmetic sequence, determine x and the next 2 terms.
----------------------------------------------------


<pre>
In arithmetic progression the difference between consecutive terms is a constant value. 
So, make a difference of the second and first terms and equals it to the difference between the third and the second terms.

Your equation is 

(-2x +4) - (x+1) = (x+15) - (-2x+4).

Simplify and solve it:

-3x + 3 = 3x + 11,

-6x = 8,

x = {{{-8/6}}} = {{{-4/3}}}.

The terms are 

1-st:  x+1 = {{{-4/3+1}}} = {{{-1/3}}},

2-nd:  -2x+4 = {{{-2*(-4/3)+4}}} = {{{8/3+4}}} = {{{20/3}}},

3-rd:  x + 15 = {{{-4/3+15}}} = {{{41/3}}}.

These are really the terms of the arithmetic progression with the difference {{{21/3}}} = 7.

Now you can easily calculate the 4-th and 5-th terms. 
</pre>