Question

the next term of the AP √48,√75,√147,..... is<br /><br />​

Answer 1

Question : -

√48 , √75 , √147 ,...

According to the question they are in AP

We can also write them like this:-

√3 x 4 x 4 , √3 x 5 x 5 , √3 x 7 x 7 ,...

So

4√3 , 5√3 , 7√3 ,...

Here , a1 = 4√3 , a2 = 5√3 and a3 = 7√3

Hence , Common Difference ( d ) = a2 - a1

=> 5√3 - 4√3

=> √3(5-4)

=> √3 x 1 = √3

But , when we calculate the Common Difference with the terms a3 and a2 , we have :-

=>7√3 - 5√3

=>√3(7-5)

=>√3(2)

=>2√3

Which is not possible for an AP

I might think that you had mistaken your question

The question should include √108 not √147

By it can form an AP

then the next term will be √147.

Hope it helped you...