Question

next term of AP √2, √8, √18​

Answer 1

Answer:

Correct option is

B

32

Given sequence 2,8,18,...

We know that 8=22,18=32

Hence the sequence can be rewritten as 2,22,32,...

Answer 2

Answer:

The next term of AP √2, √8, √18​ is √32

Step-by-step explanation:

The given arithmetic progression is √2, √8, √18​ ...

         first term, a = √2

       second term = √8 = √(4×2) = 2√2

           third term =√18 = √(9×2) = 3√2

then,

  common difference, d = 2√2 - √2 = √2

the formula to find the nth term of an AP is

                   $a_n = a + (n-1)d$

now we have to find fourth term,

    a₄ = √2 + (4-1)√2

⇒      = √2 + 3√2

⇒      = 4√2

⇒      =√(4×4×2)

⇒      =√32

the required answer is √32