Question

Consider the arithmetic sequence:

3,5,7,9,..,
If n is an integer, which of these functions generate the sequence?
Choose all answers that apply:
a(n)=3+2n for n≥0
b(n)=3n for n≥1
c(n)=-1+2n for n≥2
d(n)=-6+3n for n≥3

Answer 1

The functions that generate the given arithmetic sequence are a(n) = 3 + 2n for n ≥ 0 and b(n) = 3n for n ≥ 1.

Step-by-step explanation:

The arithmetic sequence given is 3, 5, 7, 9, ...

a) The function a(n) = 3 + 2n for n ≥ 0 generates the sequence. By substituting n = 0, 1, 2, 3, ... into the function, we get the sequence 3, 5, 7, 9, ...

b) The function b(n) = 3n for n ≥ 1 also generates the sequence. By substituting n = 1, 2, 3, 4, ... into the function, we get the sequence 3, 6, 9, 12, ...

c) The function c(n) = -1 + 2n for n ≥ 2 does not generate the sequence. By substituting n = 2, 3, 4, 5, ... into the function, we get the sequence 1, 3, 5, 7, ...

d) The function d(n) = -6 + 3n for n ≥ 3 does not generate the sequence. By substituting n = 3, 4, 5, 6, ... into the function, we get the sequence 3, 6, 9, 12, ...

The functions that generate the given arithmetic sequence are a(n) = 3 + 2n for n ≥ 0 and b(n) = 3n for n ≥ 1.