Question

Find the 6th term in the sequence

Answer 1

`a_1=1\\a_2=1\\a_n=a_(n-2)+a_(n-1)\\\\therefore\\\\a_3=a_(3-2)+a_(3-1)=a_1+a_2\to a_3=1+1=2\\\\a_4=a_(4-2)+a_(4-1)=a_2+a_3\to a_4=1+2=3\\\\a_5=a_(5-2)+a_(5-1)=a_3+a_4\to a_5=2+3=5\\\\a_6=a_(6-2)+a_(6-1)=a_4+a_5\to a_6=3+5=8`

Answer: 8

It's the Fibonacci sequence:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...