Question

Find $23\text{rd}$ of the AP: sequence is $7,5,3,1,...$

Answer 1

Step 1. Find the common difference:

The sequence is $7,5,3,1,...$.

Here, the first term $a_1=7,a_2=5,a_3=3$.

The common difference of AP is,

$\begin{array}{rcl}& \Rightarrow & d=a_2-a_1\\ & =& 5-7\\ & =& -2\end{array}$

Step 2. Calculate the $23\text{rd}$ term of the sequence :

Formula:

The general term of AP is $\begin{array}{rcl}{a}_n& =& a+\left(n-1\right)d\end{array}$, where $a$ is the first term and $d$ is the common difference.

$\begin{array}{rcl}& \Rightarrow & a_{23}=7+(23-1)\left(-2\right)\\ & =& 7-44\\ & =& -37\end{array}$

Therefore, the $23\text{rd}$ term of the sequence is $-37$.