Question

Find the next term of the ap root 27 root 48 root 75

Answer 1

Root 27 = 3 root 3
Root 48 = 4 root 3
Root 75 = 5 root 3

Next terms will be 6 root 3, 7 root 3 and so on.....
That is

6 root 3 = Root 108
7root 3 =Root 147

And so on....
Therefore next terms are

Root 108, Root, 147 and so on.

Hope this is helpful.

Answer 2

Answer:

The next term is √108  

Step-by-step explanation:

Given AP = √27, √48, √75  

here given terms can be written as shown below

   √27 = √(3×9)  = 3√3   [ ∵ √9 = 3 ]

  √48 = √(3×16)  = 4√3   [ ∵ √16 = 4 ]

  √75 = √(3×25)  = 5√3   [ ∵ √25 = 5 ]  

Therefore, given AP = 3√3, 4√3, 5√3....

As we know that general form of AP = a, a+d, a+2d, a+3d  

from given AP   T₁ = a = 3√3  

                          T₂ = a+d = 4√3

                          T₃ = a + d =  5√3    

Here we need to find next term T₄ = a+3d  

From T₁ and T₂, common difference =>  a+d-a = 4√3 - 3√3 =  

                                                                        d = √3    

Now substitute  d = √3 in T₂ ⇒ a +√3 = 4√3  

                                                            a = 4√3 - √3

                                                            a = 3√3  

Therefore, next term  T₄ = a+3d = 3√3 + 3(√3 )

                                                     = 6√3 = √(36×3) = √108