If x, 2x+9, 4x+3 are three consecutive terms of an A.P., then the value of x is :
Get the complete, step-by-step math solution for: "If x, 2x + 9, 4x + 3 are three consecutive terms of an A.P., then the value of x is :". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Understand the property of an A.P.
In an Arithmetic Progression (A.P.), the difference between any two consecutive terms is constant. If a, b, and c are three consecutive terms of an A.P., then the common difference can be expressed as b - a or c - b. Therefore, b−a=c−b. This can also be written as 2b=a+c.
Step 2: Substitute the given terms into the A.P. property
Given the three consecutive terms as x, 2x+9, and 4x+3, we can substitute these into the property 2b=a+c. Here, a=x, b=2x+9, and c=4x+3.
Step 3: Simplify the equation
First, distribute the 2 on the left side of the equation: 2(2x)+2(9)=4x+18. On the right side, combine the like terms: x+4x=5x. So, the right side becomes 5x+3.
Step 4: Solve for x
To isolate x, subtract 4x from both sides of the equation and subtract 3 from both sides of the equation. This gives 18−3=5x−4x, which simplifies to 15=x.