geometric sequence

√2, √10, 5√2...

 

5√2 = √(2 * 5²) = √50

 

The pattern is multiplying by 5 inside the square root.

 

To find the nth term, it would be:  nth term = √(2 * 5^{(n - 1)})

 

This means the 7th term = √(2 * 5^{(7 - 1)})

                                        = √(2 * 5⁶)

                                        = √(2 * 15625)

                                        = √31250, which is your answer :)