Answer :
the sequence starts at 10 and increases by 7 each time, thefore a possible sequence identification is:
[tex]\begin{gathered} a_n=7n+3 \\ \text{Let's verify:} \\ a_1=7(1)+3=7+3=10 \\ a_2=7(2)+3=14+3=17 \\ a_3=7(3)+3=21+3=24 \\ \text{and so on} \\ \text{.} \\ \text{.} \\ \text{.} \end{gathered}[/tex]Therefore, the 100th term is:
[tex]a_{100}=7(100)+3=700+3=703[/tex]