Yes, √2, √8, √18, √32... is an arithmetic progression (AP).
Understanding Arithmetic Progressions (AP)
An arithmetic progression is a sequence of numbers where the difference between any two consecutive terms is constant. This constant difference is known as the common difference. The reference states that "an arithmetic progression is a series of numbers that have a common difference."
Verifying the Given Sequence
Let's simplify the terms of the sequence:
- √2 = √2
- √8 = √(4 * 2) = 2√2
- √18 = √(9 * 2) = 3√2
- √32 = √(16 * 2) = 4√2
Now, we have the sequence: √2, 2√2, 3√2, 4√2
To check if it's an AP, we need to see if the difference between consecutive terms is constant:
- 2√2 - √2 = √2
- 3√2 - 2√2 = √2
- 4√2 - 3√2 = √2
Since the difference between consecutive terms is consistently √2, the sequence is indeed an arithmetic progression.
Next Terms
As indicated in the reference, the next two terms can be found by following the arithmetic progression pattern:
- Next term after 4√2 = 5√2 = √(25 * 2) = √50
- Term after √50 = 6√2 = √(36 * 2) = √72
