IF THERE ARE 30 PEOPLE IN YOUR CLASS ALL HAVE TO DO HAND SHAKES WITH EACH FIND TOTAL NO.OF HAND SHAKES
Answers
Answer:
There are total 30 students
The 1st student will shake hands with 29 others
The 2nd with remaining 28 since he has already shaken hands with the 1st one
Similarly the 3rd with 27 and so on till the last one has 1 person left for handshake.
Thus Total Handshakes will be
29+28+27.........+3+2+1
U can simply calculate it but it would be too tedious. So for that we have another formula in Progressions and Series. We can calculate it with the formula for Summation of an Arithmetic Progresson (A.P.)
The Series thus would be 1,2,3,……..28,29
1st term (a) =1
Common Difference (d) = 1
Total no. Of terms (n) = 29
Thus Sum of the terms (Sn) would be
Sn=[n(2a+(n−1)d)]/2
=29(2+28)/2
=435
HERE IS YOUR ANSWER :
There are total 30 students
The 1st student will shake hands with 29 others
The 2nd with remaining 28 since he has already shaken hands with the 1st one
Similarly the 3rd with 27 and so on till the last one has 1 person left for handshake.
Thus Total Handshakes will be
29+28+27.........+3+2+129+28+27.........+3+2+1
U can simply calculate it but it would be too tedious. So for that we have another formula in Progressions and Series. We can calculate it with the formula for Summation of an Arithmetic Progresson (A.P.)
The Series thus would be 1,2,3,……..28,291,2,3,……..28,29
1st term (a) =11
Common Difference (d) = 11
Total no. Of terms (n) = 2929
Thus Sum of the terms (Sn) would be
Sn=[n(2a+(n−1)d)]/2Sn=[n(2a+(n−1)d)]/2
=29(2+28)/2=29(2+28)/2
=435=435