Question

Find x so that 2x, 3x + 2, and 5x + 3 are consecutive terms of an arithmetic sequence

Short answer

The value of x=1

Step-by-step solution

Given information 

three terms are 2x, 3x + 2, and 5x + 3

Difference

$$\begin{gathered} a_1=2x \\ {a}_2=3x+2 \\ d=a_2-a_1=3x+2-2x=x+2 \\ {a}_3=5x+3 \\ d=a_3-a_2=5x+3-(3x+2)=2x+1 \end{gathered}$$

constant difference

Arithmetic sequence have common difference , so make the 'd' equal and solve for x

$$\begin{gathered} d=x+2 \\ d=2x+1 \\ x+2=2x+1 \\ x+2-2x=1 \\ -x+2=1 \\ -x=1-2 \\ -x=-1 \\ x=1 \\ thevalueofx=1 \end{gathered}$$