Question

Find the 6th term in the sequence that is defined as follows a1= 1 a2= 1 a^n= a^n-2+a^n-1

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, ...