jmc

Since the successive terms of the sequence increase by $3,$ we relate the sequence to nearby multiples of $3$ and display the table below. Compare each of the terms of the sequence with the multiple of $3$ directly below it. Notice that each term of the sequence is $2$ less than the corresponding multiple of $3$ directly below it. Since the $100^{\text{th}}$ multiple of $3$ is $300,$ the corresponding term of the sequence is $300-2=\boxed{298}.$ $$\begin{array}{ccccccc}\text{order of terms}& 1& 2& 3& 4& \dots & 100\\ \text{terms of sequence}& 1& 4& 7& 10& \dots & ?\\ \text{multiples of 3}& 3& 6& 9& 12& \dots & (300)\end{array}$$