Question

if root 2,root 8, root 18, root 32 in AP? if yes,find 2 more ters

Answer 1

√2 = √2

√8 = √2 × 2 × 2 = 2√2

√18 = √2 × 3 × 3 = 3√2

√32 = √2 × 2 × 2 × 2 × 2 = 4√2

Here,

T1 = √2 , T2 = 2√2 , T3 = 3√2 and T4 = 4√2.

Common difference ( D ) = T2 - T1 = 2√2 - √2 = √2.

Also,

Common difference ( D ) = T3 - T2 = 3√2 - 2√2 = √2.

As we know that, Common difference of an AP is always equal.

________________


√2 , √8 , ✓18 and √32

Here,

Common difference is √2.

So,

√2 , √8 , √18 and √32 in AP.

Next two terms are 5√2 and 6√2.

Answer 2

root 2 , root 8 , root 18 nd root 32.

root 2 , root 2*2*2 , root 2*3*3 nd root 2*2*2*2*2.

root 2 , 2root 2 , 3root 2 nd 4root 2.


common difference = 2root 2 - root 2 = root2.

common difference = 3root 2 - 2root 2= root2.

common difference is same .

therefore, root 2 , root 8 , root 18 and root 18 are in an ap.