Question

If root 8 , root 18, root 32, are in A.P. Find the next term and the common difference

Answer 1

root 8 = 2root 2
root 18 =3root 2
root32 =4root 2
common difference = 4root 2 - 3root 2=root2
next term = 5root2 = root50

Answer 2

The next term is $\bold{\sqrt{50}}$ and the common difference is $\bold{\sqrt{2}}$

Step-by-step explanation:

The general sequence of terms in AP are a, a+d, a+2d, a+3d…..  

Where, ‘a’ is the first term and ‘d’ is common difference between any two terms.

Every term in the sequence will be the sum of common difference and the previous term.

The given series can be written as follows:

$\sqrt{4 \times 2}, \sqrt{9 \times 2}, \sqrt{16 \times 2}, \ldots \ldots$

$\sqrt{4} \sqrt{2}, \sqrt{9} \sqrt{2}, \sqrt{16} \sqrt{2}, \ldots \ldots$

$2 \sqrt{2}, 3 \sqrt{2}, 4 \sqrt{2}, \ldots \ldots$

Here, $a=2 \sqrt{2}$

Common difference:

$d=a_{3}-a_{2} \text { or } a_{2}-a_{1}=3 \sqrt{2}-2 \sqrt{2}=4 \sqrt{2}-3 \sqrt{2}=\sqrt{2}$

The next term (here fourth term) will be $4 \sqrt{2}+\sqrt{2}$ (third term + common difference)

$\text{Fourth term} =5 \sqrt{2}=\sqrt{25 \times 2}=\sqrt{50}$