What is the closed linear form of the sequence 3,4,5,6,7,...?
A) an=2+n
B) an=2-n
C) an=3+n
D) an=3-n
Step-by-step explanation:
This is an arith. sequence.
The first term is 3 and the common difference is 1
Thus, the general formula for the nth term of this sequence is:
a(n) = 3 + 1(n - 1) This matches Answer A
To find the closed linear form of the sequence 3, 4, 5, 6, 7, ... let's analyze the pattern first.
We can observe that each term in the sequence is obtained by adding 1 to the previous term. This means that the sequence follows a linear pattern.
To find the closed linear form, we need to express the relationship between the term number (n) and the value of the term (an).
In this case, the first term (a1) is 3, which means when n = 1, a1 = 3.
Now, we can determine the equation by noticing that each term is obtained by adding (n - 1) to the first term (a1).
Therefore, the closed linear form of the sequence is an = 3 + (n - 1).
Simplifying the equation, we get an = 2 + n.
So, the correct answer is option A) an = 2 + n