Name: General Term of an AP: Example
Uploaded: 2019-07-19
Duration: 4 min 25 s
Description: Do you know how to find the first five terms of a sequence in A.P with the help of any two given terms of the sequence? Watch this video to learn how.

Question

Show the number

\sqrt{3}

on the number line.

Accepted Answer

Consider a point P on the number line such that $O P = 1$ unit and draw a line $m$ perpendicular to the number line such that $P S = 1$ unit.

Applying Pythagoras theorem, we get, $O S^{2} = O P^{2} + P S^{2}$

$O S = \sqrt{2}$ unit.

Draw an arc with centre $O$ and radius $O S$ . Mark the point of intersection of the number line and the point as $Q$ such that $O Q = \sqrt{2}$ unit.

Represent a point $Q$ such that $Q = \sqrt{2}$ on the number line.

Draw a line $l$ perpendicular to the number line through the point $Q$

Take a point $R$ on the line $l$ such that it is at unit distance from $Q$ on the line.

Draw a segment $O R$ such that a right angled triangle $∆ O R Q$ is formed.

Now, using Pythagoras theorem,

$O R^{2} =$ $O Q^{2} + Q R^{2}$

$O R^{2} = {(\sqrt{2})}^{2} + 1^{2}$

$O R^{2} = 3$ or $O R = \sqrt{3}$

Draw an arc with centre $O$ and radius $O R$ . Mark the point of intersection of the line and the arc as $C$ .

The point $C$ shows the number $\sqrt{3}$

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