Question

Write the next terms of the A.P. :

 √27, √48, √75, ...........

Answer 1

√27 = 3√3
√48 = 4√3
√75 = 5√3 .

Common difference = 4√3 - 3√3 = √3 .

Next term = 5√3 + √3 = 6√3 = √108 .

Therefore, next term is √108.

Answer 2

\(\sqrt{27} , \sqrt{48} , \sqrt{75}\) ......A.P.

\(3\sqrt{3} , 4\sqrt{3} , 5\sqrt{3}\) ......A.P.

First term : \(a=3\sqrt{3}\) 

Common Difference : \(d=a_{2}-a_{1}\) 

\(d=4\sqrt{3}-3\sqrt{3}\)

\(d=\sqrt{3}\)

n th term of an A.P. is ,

\(a_{n}=a+(n-1)d\)

4th term of A.P. is

\(a_{4}=a+3d\)

Substitute the values of a and d

\(a_{4}=(3\sqrt{3})+3(\sqrt{3})\)

\(a_{4}=6\sqrt{3}\)