The next term of the A.P.: √6, √24, √54 is: b. 196 c. √72 d. √216 a. √60

The given sequence is an Arithmetic Progression (A.P.) where each term is the square root of a number.

Step 1: Identify the common difference The common difference (d) in an A.P. is the difference between any two consecutive terms.

√24 - √6 = √24 - √6 = 2√6 √54 - √24 = √54 - √24 = 2√6

So, the common difference (d) is 2√6.

Step 2: Find the next term The next term in an A.P. is given by the formula: next term = last term + common difference.

So, the next term = √54 + 2√6 = √54 + √24 = √78

But √78 is not in the options.

Let's check if we made a mistake in our calculations. The given sequence is √6, √24, √54. If we square these numbers, we get 6, 24, 54. The differences between these numbers are 18 and 30, not a constant difference.

So, the given sequence is not an Arithmetic Progression (A.P.). There seems to be a mistake in the question.