Question

Determine x so that x-2 4x-1 and 5x+2 are three consecutive terms of an ap

Answer 1

Answer:

x = 1

Step-by-step explanation:

to say that a series is in AP the common difference should be equal

a2 - a1 = a3 - a2

x - 2 = a1

4x - 1 = a2

5x + 2 = a3

$(4x - 1) - (x - 2) = (5x + 2) - (4x - 1) \\ 4x - 1 - x + 2 = 5x + 2 - 4x + 1 \\ 3x + 1 = x + 3 \\ 3x - x = 3 - 1 \\ 2x = 2 \\ x = \frac{2}{2} \\ x = 1$

verification

x - 2 = 1 - 2 = -1

4x - 1 = 4(1) - 1 = 4 - 1 = 3

5x + 2 = 5(1) + 2 = 5 + 2 = 7

the AP is -1, 3, 7

common difference

a2 - a1 = a3 - a2

3 - (-1) = 7 - 3

3 + 1 = 7 - 3

4 = 4

hope you get your answer