Question

Q: If there are 30 students in a classroom and have been given a task to do.
The Task: Give a shake hand to each other and everyone.

Your Task: Find the total number of shake hands gone in that classroom

Answer 1

Answer:

$there \: are \: 30 \: students \: in \: the \: class \\ \\ so \: one \: student \: shake \: hand \: to \: \\ 29 \: other \: stuents \:and \: second \: \\ student \: shake \: with \: 28 \: others \\ \\ so \: total \: handshake \: series \: will \: be \\ \\ \\ 29 + 28 + 27............ + 2 + 1 \\ \\ sum \: = \frac{29}{2} (2 \times 1 + (29 - 1) \times 1) \\ \\ \: = \frac{29}{2} (30) \\ \\ \: = 29 \times 15 \\ \\ \: = 435 \\ \\ so \: total \: 435 \: handshake \: occurs$

$\huge\mathfrak\red{answer\:=435}$

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

Sum of first n terms of an arithmetic progression $= \displaystyle \: \frac{n}{2} [2a + (n - 1)d ]$

Where First term = a

Common Difference = d

GIVEN

If there are 30 students in a classroom and have been given a task to shake hand to each other and everyone.

TO DETERMINE

TO Find the total number of shake hands gone in that classroom

CALCULATION

The first student will shake hand with 29 students ( Since he cannot shake hand with himself)

The second student will shake hand with 28 students ( Since he already shake hand with first student )

The third student will shake hand with 27 students ( Since he already shake hand with first & second student )

And so on

So the total number of shake hands gone in that classroom

=

$29 + 28 + 27 + .......... + 3 + 2 + 1$

It is a arithmetic progression with

First term = a = 29

Common Difference = d = 28 - 29 = - 1

Hence the total number of shake hands gone in that classroom

$= \displaystyle \: \frac{29}{2} \{ \: 2 \times 29 + (29 - 1) \times ( - 1) \}$

$= \displaystyle \: \frac{29}{2} (58 - 28) = \frac{29}{2} \times 30 = 29 \times 15 = 435$