An arithmetic n geometric sequence have the same first term 2.with the 2nd term x. the sum of the 3rd term of the AS is equal to the 3rd term of the GS.

Give the first 3 terms of both sequences.

The square root of x+3=9-x

To find the first three terms of both the arithmetic and geometric sequences, we will need to define the common difference (d) for the arithmetic sequence and the common ratio (r) for the geometric sequence.

Let's start with the arithmetic sequence:

In an arithmetic sequence, the difference between any two consecutive terms is always the same. Since the first term is 2 and the second term is x, the common difference can be calculated as follows:

Common Difference (d) = second term - first term
= x - 2

So, the arithmetic sequence can be expressed as:
1st term = 2
2nd term = x
3rd term = 2 + (x - 2) = x

Now, let's move on to the geometric sequence:

In a geometric sequence, each term after the first is found by multiplying the previous term by a constant called the common ratio. Since the first term is 2 and the second term is x, the common ratio can be calculated as follows:

Common Ratio (r) = second term / first term
= x / 2

So, the geometric sequence can be expressed as:
1st term = 2
2nd term = x
3rd term = x * (x / 2) = (x^2) / 2

Therefore, the first 3 terms of the arithmetic sequence are 2, x, and x, while the first 3 terms of the geometric sequence are 2, x, and (x^2)/2.