Question 1181280
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You have received, to this point, three responses from different tutors, all showing either valid complete algebraic solutions, or at least a way to set up the problem for solving.<br>
All of those responses use the same approach: the difference between the first and second terms is the same as the difference between the second and third terms, and it is the same as the difference between the third and fourth terms.<br>
Many times it is worthwhile to take a close look at the given information to see if there is a quick path to the answer, before plunging into the algebra.<br>
There is an easier path to the solution to this particular problem.<br>
The second term is a-b; the fourth term is a-3b.  The difference between the second and fourth terms, -2b, is twice the common difference -- so the common difference is -b.<br>
The first term is 2, and the second term is a-b.  Since we know the common difference is -b, a is 2.<br>
To find b, we know adding the common difference to the second term will give the third term:<br>
{{{(2-b)+(-b)=2a+b+7}}}
{{{(2-b)-b=2(2)+b+7}}}
{{{2-2b=11+b}}}
{{{-9=3b}}}
{{{b=-9/3=-3}}}<br>
ANSWER: a=2; b=-3<br>