#1**0 **

I am assuming this is a geometric sequence because of the title of the post.

You can find the common ratio, by dividing the second term by the first term. \(\text{Common ratio} = \dfrac{\sqrt{10}}{\sqrt2} = \sqrt{\dfrac{10}2} = \sqrt5\).

Since the nth term of a geometric sequence is \(ar^{n - 1}\) where a is the first term and r is the common ratio, you can now substitute a = sqrt(2), r = sqrt(5), n = 7 to get the value of the 7th term.

MaxWong May 3, 2022