Question

Very-Short and Short-Answer Questions

If the numbers a, 9, b, 25 form an AP, find a and b. [CBSE 2014]

Answer 1

It is given that the numbers a, 9, b, 25 form an AP.
$\therefore 9-a=b-9=25-b$
So,
$$\begin{gathered} b-9=25-b \\ \Rightarrow 2b=34 \\ \Rightarrow b=17 \end{gathered}$$
Also,
$$\begin{gathered} 9-a=b-9 \\ \Rightarrow a=18-b \\ \Rightarrow a=18-17\left(b=17\right) \\ \Rightarrow a=1 \end{gathered}$$

Hence, the required values of a and b are 1 and 17, respectively.