Question

Given the first three terms of a linear sequence: 3x – 2;x+9; 2x + 5 Determine the value of x.​

Answer 1

x = 5

Explanation:

Each new term is 1 greater than the previous term. Therefore:

x + 9 = (3x - 2) + 1 Equivalent to x + 9 = 3x - 2 + 1, or:

9 + 2 - 1 = 2x, or 2x = 10

Thus, x = 5

Check by substituting 5 for x as indicated:

3x - 2 becomes 13 (which means the next term must be 14)

x + 9 becomes 14, and

2x + 5 becomes 15

and these consecutive sequence terms are {13, 14, 15}

Answer 2

x = 5

Explanation:

The difference between consecutive terms will be equal , then

a₂ - a₁ = a₃ - a₂ , that is

x + 9 - (3x - 2) = 2x + 5 - (x + 9) ← distribute parenthesis on both sides

x + 9 - 3x + 2 = 2x + 5 - x - 9 , simplify both sides

- 2x + 11 = x - 4 ( subtract x from both sides )

- 3x + 11 = - 4 ( subtract 11 from both sides )

- 3x = - 15 ( divide both sides by - 3 )

x = 5