Given a1=8, a2=−5, and an+1=an+2−4an. The value of a3+a4 is ....
Explanation
Given the recursive equation:
an+1=an+2−4an
We can rearrange the equation to find an+2:
an+2=an+1+4an
Step 1: Find the value of a3 by substituting n=1. Given a1=8 and a2=−5.
a1+2=a1+1+4a1
a3=a2+4a1
a3=−5+4(8)
a3=−5+32
a3=27
Step 2: Find the value of a4 by substituting n=2.
a2+2=a2+1+4a2
a4=a3+4a2
a4=27+4(−5)
a4=27−20
a4=7
Step 3: Calculate the sum a3+a4.
a3+a4=27+7
a3+a4=34
So, the value of a3+a4 is 34.