Question

If $a,b,c,d,e$ are in arithmetic progression then the value of $a+b+4c-4d+e$ in terms of $a$, if possible is

• A. $4a$
• B. $2a$
• C. $3$
• D. None of these

Answer 1

The correct option is D

None of these

Explantion for the correct option:

Find $\mathit{a}\mathbf{+}\mathit{b}\mathbf{+}\mathbf{4}\mathit{c}\mathbf{-}\mathbf{4}\mathit{d}\mathbf{+}\mathit{e}$:

Given $a,b,c,d,e$ are in arithmetic progression (AP).

Let $D$ be the common difference of (AP).

$\begin{array}{cc}\Rightarrow b=a+D,\begin{array}{rl}c& =a+2D\end{array},\begin{array}{rl}d& =a+3D\end{array},\begin{array}{rl}e& =a+4D\end{array}& \end{array}$

$\begin{array}{rl}a+b+4c–4d+e& =a+a+D+4(a+2D)–4(a+3D)+a+4D\\ & =3a+D\end{array}$

Since it cannot be expressed in terms of $a$.

Hence, option $\left(D\right)$ is the correct option.