Question

If $a , b , c , d , e , f$ are in 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

Answer: (C)

$2 ( d - c )$

Answer 2

$a , b , c , d , e , f$are in A.P.

So $b - a = c - b = d - c = e - d = f - e = K$

Where $K$ is a common difference.

Now, $d - c = e - d$ $\Rightarrow$ $e + c = 2 d$.

$e - c + 2 c = 2 d \Rightarrow e - c = 2 ( d - c )$ .

Trick : Check by putting $a = 1 , b = 2 , c = 3 , d = 4 , e = 5$

and $f = 6$ .