Question

Find the $10\text{th}$ term of the AP: sequence is$-5,\frac{-5}{2},0,\frac{5}{2}.....$

Answer 1

Step 1. Find the common difference:

The sequence is $-5,\frac{-5}{2},0,\frac{5}{2}.....$.

Here, the first term $a_1=-5,a_2=-\frac{5}{2},a_3=0$,

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

Step 2. Calculate the $10\text{th}$ 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.

$\begin{array}{rcl}& \Rightarrow & a_{10}=-5+(10-1)\frac{5}{2}\\ & =& -5+\frac{45}{2}\\ & =& \frac{35}{2}\\ & =& 17.5\end{array}$

Therefore, the $10\text{th}$ term of the sequence is $17.5$.