+153 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.
+1365 We can probably write some equations with the information we have.
We have:
\(a_n = a_{n - 1} + a_{n - 2}\) Subtracting both sides by a_n-1, we have
\(a_{n-2}=a_n-a_{n-1}\)
Now, let's plug in numbers we are given in the question. Plugging in 11 gets us \(a_9=4-1=3\)
Plugging in 10 gets us \(a_8=1-3=-2\)
Ok, let's see what happens when we plug in 9.
We get \(a_7 = a_9 - a_8\). We already know these two values!
We have \(a_7=3-(-2)=5\)
Now, we plug in 8. We get \(a_6=-2-5=-7\)
So -7 is our final answer.
Thanks! :)
+1365 We can probably write some equations with the information we have.
We have:
\(a_n = a_{n - 1} + a_{n - 2}\) Subtracting both sides by a_n-1, we have
\(a_{n-2}=a_n-a_{n-1}\)
Now, let's plug in numbers we are given in the question. Plugging in 11 gets us \(a_9=4-1=3\)
Plugging in 10 gets us \(a_8=1-3=-2\)
Ok, let's see what happens when we plug in 9.
We get \(a_7 = a_9 - a_8\). We already know these two values!
We have \(a_7=3-(-2)=5\)
Now, we plug in 8. We get \(a_6=-2-5=-7\)
So -7 is our final answer.
Thanks! :)
