Question

what is the next term of the ap √2√8√18

Answer 1

Given sequence is √2 , √8, √18,...

a1 = √2 ,

a2 = √8 = √ ( 2 × 2 ) ×2 = 2√2

a3 = √18 = √ ( 3 × 3 ) × 2 = 3 √2

First term (a ) = a1 = √2

a2 - a1 = 2√2 - √2 = √2

a3 - a2 = 3√2 - 2√2 = √2

Therefore ,

a2 - a1 = a3 - a2 = √2

Common difference (d) = √2

The given sequence is in A.P .

nth term = an = a + ( n-1 ) d

14th term of the A.P = a4

a4 = a + ( 4 - 1 ) d

= a + 3d

= √2 + 3 × √18

= √2 + 3√2

= 4√2

4th term of the given A.P = 4√2

Or

a4 = 4√2

#BeBrainly

Answer 2

Answer:

The next term of the given arithmetic progression is $4\sqrt{2}$.

Step-by-step explanation:

The given sequence is : $\sqrt{2},\sqrt{8},\sqrt{18}$

First term $a_{1} =\sqrt{2}$

$a_{2} = \sqrt{8} =\sqrt{2*2*2} = 2\sqrt{2}$

$a_{3} =\sqrt{18} = \sqrt{3*3*2} =3\sqrt{2}$

To find the common difference d of the given A.P :

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

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

Therefore the common difference d is $\sqrt{2}$.

Hence the fourth term of the A.P would be :

$a_{3}+d= 3\sqrt{2} + \sqrt{2} =4\sqrt{2}$

Hence the fourth term is $4\sqrt{2}$.