Question

What is the $n^{th}$ term of a sequence?

Answer 1

General term of a sequence:

$n^{th}$ term of an arithmetic sequence:

• The general form of an AP: $a,a+d,a+2d,a+3d,.....$, where $a$ is the first term and $d$ is a common difference.
• The formula for $n^{th}$ term: $a_n=a+\left(n-1\right)d$

$n^{th}$ term of a geometric sequence:

• The general form of a GP: $a,ar,a{r}^2,a{r}^3,.....$, where $a$ is the first term and $r$ is a common ratio.
• The formula for $n^{th}$ term: $a_n=a{r}^{n-1}$

$n^{th}$ term of a harmonic sequence:

• The general form of a HP: $\frac{1}{a},\frac{1}{a+d},\frac{1}{a+2d},\frac{1}{a+3d},.....$, where $a$ is the first term and $d$ is a common difference.
• The formula for $n^{th}$ term: $a_n=\frac{1}{a+\left(n-1\right)d}$