1. The first of the 7 people will shake hands with 6 others. Only 6 because no person is going to shake hands with themselves. The second person also shakes hands with 6 people, but you have already counted one of those handshakes, namely the one with the first person. Therefore, the second person shakes hands with only 5 NEW people. Then the third person adds 4 new handshakes, etc., down to the 2nd to the last person who adds 1 new handshake. The last person has no one new, so all of the last person's handshakes are already counted. In summary: 6+5+4+3+2+1 7·6/2 = 21
2. The Fibonacci Sequence is the series of numbers:
the next number is found by adding up the two numbers before it; so,
the next number is ++5%2B+8=13, then 8%2B13=21,13%2B21=34, and so on
0, 1, 1,+2, 3, 5,+8, 13,+21, 34, ... (Citings-Algebra.com)
