Find the next 3 terms of the seqence $1,2,\sqrt{7}, \sqrt{10}, \sqrt{13}, 4, \cdots $

Question

How do you find the next 3 terms of the sequence $1,2,\sqrt{7}, \sqrt{10}, \sqrt{13}, 4, \cdots $? I have not been able to even determine the type of sequence (arithmetic, geometric, or harmonic).

Answer 1

This sequence works :

$$u_n = \sqrt{ 1+3n }$$

Answer 2

Hint:

The sequence is the same as

$$\sqrt{1}\quad \sqrt{4} \quad \sqrt{7} \quad \sqrt{10} \quad \sqrt{13} \quad \sqrt{16}\quad \ldots$$

Answer 3

$$\sqrt 1,\sqrt 4,\sqrt 7,\sqrt{10},\sqrt{13},\sqrt{16},\cdots$$ Can you see any pattern?