Question 1181280

The first four terms of an arithmetic sequence are 2, a-b, 2a+b+7, a-3b . Find a and b. 

<pre>{{{matrix(1,10, 2^(nd), term, "-", 1^(st), "=", 3^(rd), term, "-", 2^(nd), term)}}}
              {{{matrix(7,3, a - b - 2, "=", 2a + b + 7 - (a - b), a - b - 2, "=", 2a + b + 7 - a + b, a - b - 2, "=", a + 2b + 7, - 2 - 7, "=", 2b + b, - 9, "=", 3b, (- 9)/3, "=", b, - 3, "=", b)}}}
{{{matrix(1,10, 2^(nd), term, "-", 1^(st), "=", 4^(th), term, "-", 3^(rd), term)}}}
          {{{matrix(5,3, a - b - 2, "=", a - 3b - (2a + b + 7), a - b - 2, "=", a - 3b - 2a - b - 7, a - b - 2, "=", a - 2a - 3b - b - 7, a - b - 2, "=", - a - 4b - 7, a + a - b + 4b, "=", - 7 + 2)}}}
              {{{matrix(1,3, 2a + 3b, "=", 5)}}} ----- eq (i)
            2a + 3(- 3) = - 5 --- Substituting - 3 for b in eq (i)
                 2a - 9 = - 5
                     2a = 4
                     {{{highlight_green(matrix(1,5, a, "=", 4/2, "=", 2))}}}