Question

Write the value of x for which 2x, x+10 and 3x+2 are in AP.

Answer 1

Hint: In this question, we are given three terms of an arithmetic progression in terms of x and we need to find the value of x. For this, we will use the arithmetic mean property. According to the arithmetic mean property, the sum of the first term and the third term of an arithmetic progression is equal to twice of the second term of the arithmetic progression.

Complete step by step answer:
Here we are given the three terms of an arithmetic progression as 2x, x+10, and 3x+2.
Let us suppose the first term as 2x, the second term as x+10, and the third term as 3x+2.
Now we know by the arithmetic mean property that the sum of the first term and the third term of an arithmetic progression is equal to the second term of an arithmetic progression. So we can say forgiven arithmetic progression that,
 $ 2x+\left( 3x+2 \right)=2\left( x+10 \right)\Rightarrow 2x+3x+2=2x+20 $ .
Taking variable on one side and constant on the other side we get,
 $ 2x+3x-2x=20-2\Rightarrow 3x=18 $ .
Dividing both sides by 3 we get,
 $ x=\dfrac{18}{3}=6 $ .
Hence the required value of x is 6.

Note:
Students should take care of the signs while solving this sum. Make sure to take twice of the second term. Students can also solve this sum using the common difference in an arithmetic progression i.e. the difference between the second term and the first term is equal to the difference between the third term and the second term.