Let a_1, a_2, a_3, \dots be a sequence. If
a_n = a_{n - 1} + a_{n - 2}
for all n \ge 3, and a_{11} = 4 and a_{10} = 1, then find a_6.
a11=a10+a9, so following this logic.
4=1+a9
a9=3
Similarly,
1=3+a8
a8=−2
3=−2+a7
a7=5
−2=5+a6
a6=−7.
a6 is -7.