The second, fourth and sixth terms of an Arithmetic Progression (AP.) are x – 1, x + 1 and 7 respectively. Find the:
(a) common difference;
(b) first term;
(c) value of x.
Explanation
(a) The second term is a + d= x - 1 while the fourth term is a + 3d = x + 1. Subtracting the second term from the fourth term yielded 2d = 2 so that d = 1.
(b). Substituting for d in the expression for the sixth term to get a + 5d = 7; a + 5(1) = 7 and solving for a to obtain a = 2.
(c). Substituted for a and d in the expression for the second term( a + d = x - 1) and found x = 2 + 1 + 1 = 4.