Question

find the next term of the A.P.
$\large \sf \sqrt{2},\sqrt{8},\sqrt{18}$

Answer 1

Step-by-step explanation:

Given:-

The AP is √2,√8,√18,

To find:-

Find the next term of the given AP?

Solution:-

Given AP is √2,√8,√18,

First term (a) =( t1 )= √2

Second term (t 2) = √8 =√(2×2×2)=2√2

Third term (t 3) = √18 = √(2×3×3) = 3√2

The given AP can be written as √2 , 2√2 ,3√2

Common difference (d)=tn - tn-1

=>d= 2√2-√2

=>d=(2-1)√2

=>d=√2

The common difference of the given AP = √2

We know that

The genaral or nth term of an AP is

tn= t1 +(n-1)d

The next term of the given AP

=Fourth term of the given AP

=>t4= t1+(4-1)d

=>t4 = t1+3d

On Substituting the values of t1 and d in the above equation then

t4 = √2+3√2

=>t4 = (1+3)√2

=>t4 = 4√2

or

=>t4 = √(2×4×4)

=>t4 = √32

The fourth term = √32

Answer:-

The next term if the given AP = √32

Used formulae:-

t1 is the first term, d is the common difference and n is the number of terms of an AP then

• Common difference = tn - tn-1
• General term = t1 +(n-1)d

Answer 2

The given AP is √2, √8, √18,

On simplifying the terms, we get: