+216 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.
+1950 We can probably write some equations with the information we have.
We have:
an=an−1+an−2 Subtracting both sides by a_n-1, we have
an−2=an−an−1
Now, let's plug in numbers we are given in the question. Plugging in 11 gets us a9=4−1=3
Plugging in 10 gets us a8=1−3=−2
Ok, let's see what happens when we plug in 9.
We get a7=a9−a8. We already know these two values!
We have a7=3−(−2)=5
Now, we plug in 8. We get a6=−2−5=−7
So -7 is our final answer.
Thanks! :)
+1950 We can probably write some equations with the information we have.
We have:
an=an−1+an−2 Subtracting both sides by a_n-1, we have
an−2=an−an−1
Now, let's plug in numbers we are given in the question. Plugging in 11 gets us a9=4−1=3
Plugging in 10 gets us a8=1−3=−2
Ok, let's see what happens when we plug in 9.
We get a7=a9−a8. We already know these two values!
We have a7=3−(−2)=5
Now, we plug in 8. We get a6=−2−5=−7
So -7 is our final answer.
Thanks! :)
