No, the series √3, √6, √9, √12 is not an arithmetic progression (AP).
Understanding Arithmetic Progressions
An arithmetic progression (AP) is a sequence of numbers such that the difference between any two consecutive terms is constant. This constant difference is called the common difference.
Analyzing the Given Series
Let's examine the differences between consecutive terms in the given series: √3, √6, √9, √12
- Term 1: √3
- Term 2: √6
- Term 3: √9 = 3
- Term 4: √12 = 2√3
Now, let's calculate the differences:
- Difference between Term 2 and Term 1: √6 - √3 ≈ 2.449 - 1.732 ≈ 0.717
- Difference between Term 3 and Term 2: 3 - √6 ≈ 3 - 2.449 ≈ 0.551
- Difference between Term 4 and Term 3: 2√3 - 3 ≈ 3.464 - 3 ≈ 0.464
Since the differences between consecutive terms (0.717, 0.551, 0.464) are not the same, the series is not an arithmetic progression.
Conclusion
According to the reference, the series is not an AP because the difference between consecutive terms is not the same. This analysis confirms that √3, √6, √9, √12 is indeed not an arithmetic progression.
