Question

the next term of √2,√8,√18,_ _ _ _. (a) √100 (b) √20 (c) √24 (d) √32​

Answer 1

Answer:

$\sqrt{32}$

Step-by-step explanation:

Hand writing is not so good.

Answer 2

Given :-

A sequence $\sqrt{2} , \sqrt{8} , \sqrt{18} . . . . . .$

To Find :-

The next term of the sequence .

Solution :-

Let us first see which type of sequence is This i.e Arithmetic , Geometric or Harmonic ;

The above sequence can be written as :-

$\sqrt{2} \; , 2 \sqrt{2} \; , 3 \sqrt{2} \; , . . . . .$

Here , first term = $a_1 = \sqrt{2}$

Second term = $a_2 = 2 \sqrt{2}$

Third term = $a_3 = 3 \sqrt{2}$

$a_{2} - a_{1} = 2 \sqrt{2} - \sqrt{2}$

$\Rightarrow a_{2} - a_{1} = \sqrt{2}$

$a_{3} - a_{2} = 3 \sqrt{2} - 2 \sqrt{2}$

$\Rightarrow a_{3} - a_{2} = \sqrt{2}$

Here , the common difference ( d ) is same i.e $\sqrt{2}$ so this series is an A.P series . Now ;

$a_{4} = a_{1} + 3d$

$a_{4} = \sqrt{2}  + 3.\sqrt{2}$

$a_{4} = 4 \sqrt{2}$

$a_{4} = \sqrt{ 4.4.2 }$

$a_{4} = \sqrt{32}$

Henceforth , the required answer is (d) $\sqrt{32}$