Error: The sequence is not an arithmetic sequence. Recursive Rule: a_1=2, a_2=4, a_n=a_(n-2)+a_(n-1)
Practice makes perfect
We are asked to fix the error in the recursive rule for the given sequence. Let's check if the difference between the other consecutive terms is 2.
We see that 2 is not a common difference, meaning the sequence is not an arithmetic sequence. The recursive rule written in the solution is not the correct rule.
Incorrect: & a_1=2, a_n=a_(n-1)+2 *
Let's check for a common ratio.
There is no common ratio, meaning it is not a geometric sequence. Although the sequence is neither arithmetic nor geometric, we can write a recursive rule for it. Let's look for a pattern in the sum of consecutive terms.
a_1+a_2&=2+4 =6
a_2+a_3&=4+6 =10
a_3+a_4&=6+10=16
We see that beginning with the third term each term is the sum of two previous terms. Hence, a recursive equation for the sequence is a_n=a_(n-2)+a_(n-1).
The first two terms and the recursive equation gives us the recursive rule.
Recursive Rule:
a_1=2, a_2=4, a_n=a_(n-2)+a_(n-1)
