Question

How do you find the $20$th term of an AP

Answer 1

Arithemtic progression general term:

As we know, the formula of $nth$ term of an AP is,

${\mathit{t}}_{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}\mathit{a}\mathbf{}\mathbf{+}\mathbf{}\left(n-1\right)\mathit{d}$

where, $a=$ First term of the AP

$n=$ number of terms of AP

$d=$ difference of second and first term of AP

For example; Let $10,15,20,25,...$ be an AP

Here, $a=10$ and $d=5$, then the value of $20th$ term of this AP will be,

$\begin{array}{rcl}{t}_{20}& =& a+19d\\ & =& 10+19\times 5\\ & =& 10+95\\ & =& 950\end{array}$

Hence, we can find the $20th$ term of an AP by the formula ${\mathit{t}}_{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}\mathit{a}\mathbf{}\mathbf{+}\mathbf{}\left(n-1\right)\mathit{d}$