7.6Summary and Cross-References

• A number sequence follows a rule, with terms labelled $T_1, T_2, T_3, \ldots$ by position.
• Arithmetic means a constant difference $d$; geometric means a constant ratio $r$.
• The general term $T_n$ gives any term from its position. Verify with $T_1$ and $T_2$.
• For a linear sequence, $T_n = dn + T_0$ with $T_0 = T_1 - d$.
• When the differences are not constant, compare with the square numbers, $n(n + 1)$ or the triangular numbers, position by position.
• To test whether $k$ is a term, solve $T_n = k$ and check $n$ is a positive integer.