General Term of a Number Sequence

The general term of a number sequence is one of many ways of defining sequences.

Consider the tower of bricks. The first row has five bricks on top of the pile, the second row has six bricks, and the third row has seven bricks. If $T_n$ represents the number of bricks in row $n$ (from the top) then $T_1 = 5, \ T_2 = 6, \ T_3 = 7, …$
This sequence can be specified by using an explicit formula $T_n = n + 4$ isthe general term or $n$th term formula for $n = 1, 2, 3, 4, …$.
The general term or nth term of a sequence is represented by a symbol with a subscript, for example, $u_n, \ T_n, \ A_n$. The general term is defined for $n = 1, 2, 3, 4, …$.
${u_n}$ represents the sequence that can be generated by using $u_n$ as the $n$th term.

Practice Questions of General Term

Question 1

A sequence is defined by $u_n = 2n – 3$. Find $u_9$.

Question 2

A sequence is defined by $T_n = n^2 + 1$. Find the first four terms.

Question 3

A sequence is defined by $A_n = 2^n$. Find the first four terms.