Question

What is the general term of a sequence?

Answer 1

The General Term of a Sequence:

• The general term for a sequence follows a certain pattern. The successive terms are getting by adding or multiplying a number to the previous term. Sometimes each term of the series follows an expression.
• The general term of an AP is ${\mathit{T}}_{\mathbf{n}}\mathbf{=}\mathit{a}\mathbf{+}\mathbf{(}\mathit{n}\mathbf{-}\mathbf{1}\mathbf{)}\mathit{d}$. Sequence is $a,a+d,a+2d,\cdots$ where $a$ is first term and $d$ is a common difference
• The general term of a GP is${\mathit{T}}_{\mathbf{n}}\mathbf{=}\mathit{a}{\mathit{r}}^{\mathbf{n}\mathbf{-}\mathbf{1}}$.Sequence is $a,ar,a{r}^2,\cdots$ where $a$ is the first term of GP and $r$ is common ratio.
• The general term of an HP is ${\mathit{T}}_{\mathbf{n}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{a}\mathbf{+}\mathbf{(}\mathbf{n}\mathbf{-}\mathbf{1}\mathbf{)}\mathbf{d}}$.Sequence is $\frac{1}{a},\frac{1}{a+d},\frac{1}{a+2d},\cdots$ where $a,a+d,a+2d,\cdots$ are in the AP.