Question

Find the value of ‘x’ for which $x+2,2x,2x+3$ are three consecutive terms of an AP.

Answer 1

Hint: To calculate the value of ‘x’, use the fact that the difference between any two consecutive terms of an AP is a constant. Write equations based on the data given in the question and simplify those equations to calculate the value of variable ‘x’.

Complete Step-by-step answer:
We have to calculate the value of variable ‘x’ such that $x+2,2x,2x+3$ are three consecutive terms of an AP. We know that the difference between any two consecutive terms on an AP is a constant. We will first calculate the difference between the terms $2x,2x+3$. Thus, we have $2x+3-2x=3$. We will now calculate the difference between the terms $x+2,2x$. Thus, we have $2x-\left( x+2 \right)=2x-x-2=x-2$.
We know that the difference is the same in both cases. Thus, we have $x-2=3$. Rearranging the terms of the above equation, we have $x=2+3=5$. Hence, the value of variable ‘x’ such that $x+2,2x,2x+3$ are three consecutive terms of an AP is $x=5$.

Note: We know that Arithmetic Progression (AP) is a sequence of terms such that the difference between any two consecutive terms is a constant. We can calculate the value of terms of the AP by substituting the value of ‘x’ in the terms and simplifying it.