Question

Find $11\text{th}$ of the AP: sequence is$-3,\frac{-1}{2},2,...$

Answer 1

Step 1. Find the common difference:

The sequence is $-3,\frac{-1}{2},2,...$.

Here, the first term $a_1=-3,a_2=-\frac{1}{2},a_3=2$.

The common difference of AP is,

$\begin{array}{rcl}& \Rightarrow & d=a_2-a_1\\ & =& \frac{-1}{2}-(-3)\\ & =& \frac{-1}{2}+3\\ & =& \frac{5}{2}\end{array}$

Step 2. Calculate the $11\text{th}$ 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.

$\begin{array}{rcl}& \Rightarrow & a_{11}=-3+(11-1)\frac{5}{2}\\ & =& -3+\frac{50}{2}\\ & =& 22\end{array}$

Therefore, the $11\text{th}$ term of the sequence is $22$.