Look at the following sequence:
2,221,331,441…
Which expression represents the term-to-term rule of the sequence?
To find the expression that accurately represents the sequence, let's analyze the given numbers:
- The first term is 2, which can be represented as 2+11=2+11 for n=2.
- The second term is 221=2+21, when n=2.
- The third term is 331=3+31, when n=3.
- The fourth term is 441=4+41, when n=4.
From the sequence pattern, we see that each term is indeed n+n1.
Now, let's express each choice based on n:
- Choice 1: 2n+n1 - This does not match our pattern.
- Choice 2: 0.5n1+2n+0.5n1−n - This form is complex and incorrect.
- Choice 3: Indicates there is no correct property, but we identified one.
- Choice 4: n2+n2+3n−n2−n1−2n simplifies to n+n1.
Therefore, the expression n2+n2+3n−n2−n1−2n simplifies correctly to describe the term-to-term rule of the sequence.
The solution to the problem is the expression: n2+n2+3n−n2−n1−2n.
n2+n2+3n−n2−n1−2n