The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
If (x + 1), 3x and (4x + 2) are in A.S. then the value of x is ?
Answer:
x = 3
Therefore, the value of x is 3.
Explanation:
We are given the first three terms of an arithmetic sequence.
(x + 1), 3x, (4x + 2)
The common difference (d) is the difference between two consective terms.
d = (4x + 2) - 3x
d = 4x - 3x + 2
d = x + 2
Also,
d = 3x - (x + 1)
d = 3x - x - 1
d = 2x - 1
Since the common difference must be equal so,
x + 2 = 2x - 1
Combine the like terms
2x - x = 2 + 1
x = 3
Therefore, the value of x is 3.
The values of terms are
x + 1 = 3 + 1 = 4
3x = 3(3) = 9
(4x + 2) = 4(3) + 2 = 12 + 2 = 14
4, 9, 14
As you can notice, the difference between these terms is constant.
14 - 9 = 5
9 - 4 = 5