Question

Is root 2, root 8, root 18, root 32, ..... an A.P.? If yes, then find its next 2 terms.

Answer 1

√2, √8, √18, √32,.......
√8 = 2√2
√18 = 3 √2
√32 = 4 √2
Hence,the sequence is √2, 2 √2,3 √2,4 √2
a = √2
D = 2 √2- √2
= √2
3 √2-2 √2
= √2
Since the common difference is same every time Hence given sequence is in AP
Next two terms are
4 √2+ √2 = 5 √2 = √50
5 √2 + √2 = 6 √2 = √72
Hope it helps
Mark as the BRAINLIEST

Answer 2

Yes, root 2, root 8, root 18, root 32, ...is an A.P. and the next two terms of the A.P. are √50 and √72.

Given:

An AP- √2, √8, √18, √32...

To find:

The next two terms of the A.P.

Solution:

We can find the solution by following the given steps-

We know that an arithmetic progression is a series of numbers that have a common difference.

The series is √2, √8, √18, √32...

Here, √8= √2×√2×√2= 2√2

√18=√2×√9= 3√2

√32=√2×√16= 4√2

So, the A.P. is √2, 2√2, 3√2, 4√2... with a common difference of √2.

The next two terms can be obtained as-

4√2+√2=5√2

=√25×√2=√50

and

5√2+√2=6√2

=√36×√2=√72

Therefore, the next two terms of the A.P. are √50 and √72.