How many handshakes will takes place?

Question

In a party there are 49 persons present.
If each of them shakes hand with all the other persons, in total how many handshakes will takes place?

Answer 1

Note - I am not sure of the answer this is the first time I have solved the problem. If anyone knows the solution, tell me if I am right or wrong

the first person will shake hands with 48 people
the second person will shake hands with 47 people excluding the first
and so on
until last 2 remain
so it forms an A.P
a = 48
d = -1

2 = 48 -n+1
n = 47

s = n/2*(2a+(n-1)*d)
s = 47/2 * (2*48 +(47-1)*-1)
s = 47/2 *(96 -46)
s = 47/2*(50)
s = 47*25
s = 1175

Answer 2

My previous answer was wrong by one handshake
check the answer here
https://m4maths.com/maths-puzzles.php