Question

The terms x,0.5x + 7, and 3x - 1 are consecutive terms of an arithmetic sequence. How do i determine the value of x and state the three terms

Answer 1

So you know that for arithmetic sequences, the difference between each term is the same. So we can use this to form an equation:

Difference between term 2 and 1 = Difference between term 3 and 2

$(0.5x+7)-x = (3x-1)-(0.5x+7) \\-0.5x+7=2.5x-8 \\15=3x \\x=5$

So the three values are:

5, 0.5(5)+7, 3(5)-1

= 5, 9.5, 14