Question

If $a,b,c,d,e,f$ are in Arithmetic Progression(A.P.), then the value of $e-c$ will be.

• A. $2(c–a)$
• B. $2(f–d)$
• C. $2(d–c)$
• D. $d–c$

Answer 1

The correct option is C

$2(d–c)$

Find the value of $\mathit{e}\mathbf{-}\mathit{c}\mathbf{:}$

Given that $a,b,c,d,e,f$ are in Arithmetic Progression(A.P.) Let $p$ be the common difference of given Arithmetic Progression.

$b=a+p,c=a+2p,d=a+3p,e=a+4p,f=a+5p$

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

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