If $x$, $2x + 9$, $4x + 3$ are three consecutive terms of an A.P., then the value of x is :

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 $15 = x$.

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