If $p, q, r, s, t$ and $u$ are in AP, then difference $(t - r)$ is equal to

2 (s - r)

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(u - q)

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2 (s - p)

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2 (u - q)

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Solution

The correct option is A $2 (s - r)$
Given that, $p, q, r, s, t$ and $u$ are in AP.
$∴ s - r = t - s = u - t$
By taking first two terms,
$s - r = t - s$
$\Rightarrow s - r - r = t - s - r$ [by subtracting $r$ from both sides]
$\Rightarrow s - 2 r = (t - r) - s$
$\Rightarrow 2 s - 2 r = t - r$
$∴ 2 (s - r) = t - r$ .

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