If $a, b, c, d, e, f$ are in A.P., then $(e - c)$ is equal to

2 (c - a)

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2 (d - c)

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2 (f - d)

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2 (d - c)

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Solution

The correct option is C $2 (d - c)$
Let $x$ be the common difference of the A.P. $a, b, c, d, e, f$ .

As e is the 5th term
$∴ e = a + (5 - 1) x (∵ a_{n} = a + (n - 1) d)$ , where a_n is the nth term

$\Rightarrow e = a + 4 x$ ...(1)
and $c = a + 2 x$ ...(2)

$∴$ Using equation (1) and (2), we get
$e - c = a + 4 x - a - 2 x$
$\Rightarrow e - c = 2 x = 2 (d - c)$

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If a,b,c,d,e,f are in AP then e - c is equal to what?

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