The problem states that we have an arithmetic sequence $x, x+3, 3x+2$. We need to find the first 5 terms of the sequence.

1. Problem Description

The problem states that we have an arithmetic sequence $x, x+3, 3x+2$. We need to find the first 5 terms of the sequence.

2. Solution Steps

First, we need to determine the value of $x$. Since the sequence is arithmetic, the difference between consecutive terms must be constant. Therefore,

$$(x+3) - x = (3x+2) - (x+3)$$

Simplifying the equation:

$$3 = 3x+2 - x - 3$$

$$3 = 2x - 1$$

$$4 = 2x$$

$$x = 2$$

Now that we have $x=2$, we can find the first three terms of the sequence:

First term: $x = 2$

Second term: $x+3 = 2+3 = 5$

Third term: $3x+2 = 3(2)+2 = 6+2 = 8$

The common difference $d$ is the difference between consecutive terms:

$d = 5 - 2 = 3$

$d = 8 - 5 = 3$

Now we can find the next two terms:

Fourth term: $8 + 3 = 11$

Fifth term: $11 + 3 = 14$

Therefore, the first five terms are 2, 5, 8, 11,

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3. Final Answer

The first 5 terms of the arithmetic sequence are 2, 5, 8, 11, 14.