Establish the relation Snth - u - a22n -1- where the letters have their usual meaning-

Distance traveled in (n 1) seconds, S_n 1=u(n 1)+12a(n 1)^2 Distance traveled in n seconds, S_n=u(n)+12a(n)^2 Distance traveled in nth second, =S_n ...

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Standard XII

Mathematics

Definite Integral as Limit of Sum

Establish the...

Question

Establish the relation $S_{n} t h = u + \frac{a}{2} (2 n - 1)$ , where the letters have their usual meaning.

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Solution

Distance traveled in (n-1) seconds,
$S_{n - 1} = u (n - 1) + \frac{1}{2} a (n - 1)^{2}$
Distance traveled in n seconds,
$S_{n} = u (n) + \frac{1}{2} a (n)^{2}$
Distance traveled in nth second,
$= S_{n} - S_{n - 1} = u + \frac{1}{2} a (2 n - 1)$

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Establish the relation Snth=u+a2(2n−1), where the letters have their usual meaning.

Distance traveled in (n-1) seconds,Sn−1=u(n−1)+12a(n−1)2Distance traveled in n seconds,Sn=u(n)+12a(n)2Distance traveled in nth second,=Sn−Sn−1=u+12a(2n−1)

Establish the relation $S_{n} t h = u + \frac{a}{2} (2 n - 1)$ , where the letters have their usual meaning.

Distance traveled in (n-1) seconds,
$S_{n - 1} = u (n - 1) + \frac{1}{2} a (n - 1)^{2}$
Distance traveled in n seconds,
$S_{n} = u (n) + \frac{1}{2} a (n)^{2}$
Distance traveled in nth second,
$= S_{n} - S_{n - 1} = u + \frac{1}{2} a (2 n - 1)$