If a,b,c,d,e,f are in A.P. , then value of e - c will be

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8. Sequences and Series

easy

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

$d - c$

Solution

(c) $a,\;b,\;c,\;d,\;e,\;f$ 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 = 2d$.

$e{\rm{-}}c + {\rm{2}}c = 2d $

$\Rightarrow e – c = 2(d – c)$.

Trick : Check by putting $a = 1,\;b = 2,\;c = 3,\;d = 4,\;e = 5$ and $f = 6$.

Standard 11

Mathematics

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