Question

In the given APs, find the missing terms.

$5,....,......,9\frac{1}{2}$

Answer 1

STEP-1 Finding the common difference of the given AP

Let the first term of an AP be $a$ and the common difference be $d.$

Then the general term is given by $a_n=a+\left(n-1\right)d$

We have given $5,....,......,9\frac{1}{2}$

$a=5$ $a_n=9\frac{1}{2}$ and $n=4$

Now, $a_4=5+\left(4-1\right)d$

For $n=4$, we have $a_4=9\frac{1}{2}$

$\begin{array}{rcl}& \Rightarrow & 5+\left(4-1\right)d=9\frac{1}{2}\\ & \Rightarrow & 5+3d=\frac{19}{2}\\ & \Rightarrow & 3d=\frac{19}{2}-5\\ & \Rightarrow & 3d=\frac{9}{2}\\ & \Rightarrow & d=\frac{3}{2}\end{array}$

Step 2: Finding the missing term

The missing term are $2\mathrm{nd}$ and $3\mathrm{rd}$ term of the given AP.

So,

$\begin{array}{rcl}{a}_2& =& 5+d\\ & =& 5+\frac{3}{2}\\ & =& \frac{13}{2}\end{array}$

$\begin{array}{rcl}{a}_3& =& 5+2d\\ & =& 5+2·\frac{3}{2}\\ & =& 8\end{array}$

Hence, the missing terms are $\frac{13}{2}$ and $8$