Question
If (X3), 3x (4x + 1) are in A. S. then the value of xis
(1 Point)

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 ?

x = 3

Therefore, the value of x is 3.

Step-by-step 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

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step-by-step explanation: