What is the explicit rule for the sequence -5, -3, -1, 1, …?
A.f(n) = -5 + (n – 1)(-2)
B. f(n) = 5 + (n – 1)(-2)
C. f(n) = -5 + (n – 1)(2)
D .f(n) = 5 + (n – 1)(2)
each term is 2 more than the previous term
the 1st term is -5
To find the explicit rule for the sequence -5, -3, -1, 1, …, we need to identify the pattern in the sequence.
Looking at the sequence, we can see that each term is obtained by adding 2 to the previous term. So, the common difference between each term is 2.
To find the explicit rule, we can use the formula for arithmetic sequences, which is:
f(n) = a + (n – 1)d
where f(n) represents the nth term of the sequence, 'a' is the first term, 'n' is the position of the term, and 'd' is the common difference.
In this case, the first term is -5 and the common difference is 2.
Plugging these values into the formula, we get:
f(n) = -5 + (n – 1)(2)
Simplifying further, we have:
f(n) = -5 + 2n - 2
f(n) = 2n - 7
Therefore, the explicit rule for the sequence -5, -3, -1, 1, ... is f(n) = 2n - 7.
Based on the given answer choices, the correct option is D. f(n) = 5 + (n – 1)(2).