Which term of the Geometric progression 4, 4√2, 8……64√2 ?a.12b.10c.9d.8

The given geometric progression is 4, 4√2, 8, 8√2, 16, 16√2, 32, 32√2, 64, 64√2...

The common ratio (r) of this geometric progression is 4√2 / 4 = √2.

We are asked to find which term is 64√2.

In a geometric progression, the nth term can be found using the formula a * r^(n-1), where a is the first term and r is the common ratio.

So, we can set up the equation 4 * (√2)^(n-1) = 64√2.

Solving this equation will give us the value of n.

Divide both sides by 4, we get (√2)^(n-1) = 16√2.

We can rewrite 16√2 as 2^4 * 2^(1/2) = 2^(9/2).

So, we have (√2)^(n-1) = 2^(9/2).

Since √2 = 2^(1/2), we can rewrite the left side of the equation as (2^(1/2))^(n-1) = 2^(9/2).

Simplifying, we get 2^(n-1/2) = 2^(9/2).

Since the bases are equal, the exponents must also be equal. So, n - 1/2 = 9/2.

Solving for n, we get n = 9/2 + 1/2 = 5.

So, the 5th term of the geometric progression is 64√2.

Therefore, none of the options a.12, b.10, c.9, d.8 are correct. The correct answer is 5.