Question

$\mathit{Q}\mathit{u}\mathit{e}\mathit{s}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{N}\mathit{o}\mathbf{}\mathbf{2}\mathbf{:}$

If $21,a,b,and-3$$18$ are in AP, then find the value of $(a+b).$

Answer 1

Step 1: Given information

Given that $21,a,b,and-3$ are in AP.

Then, we know that $a_2-a_1=a_3-a_2.$

Step 2: Finding the value of $\mathit{a}\mathbf{}\mathit{a}\mathit{n}\mathit{d}\mathbf{}\mathit{b}$

$$\begin{gathered} a-21=b-a \\ 2a-21=b\dots \dots \dots .\left(1\right) \end{gathered}$$

Similarly, we can write

$$\begin{gathered} b-a=-3-b \\ a-2b=3\dots \dots \dots \left(2\right) \end{gathered}$$

On solving the equations (1) and (2) we get,

$$\begin{gathered} a-2(2a-21)=3 \\ a-4a-42=3 \\ 3a=39 \\ \mathit{a}\mathbf{=}\mathbf{13} \end{gathered}$$

On substituting the value of $a$ in equation (1), we get,

$$\begin{gathered} 2\left(13\right)-21=b \\ 26-21=b \\ \mathit{b}\mathbf{=}\mathbf{5} \\ then,(a+b)=13+5=18. \end{gathered}$$

Final Answer: Therefore, the value of $(a+b)$ is 18.