Question

An arithmetic sequence has this recursive formula:

a = 9
an = 2,4-3
What is the explicit formula for this sequence?
A. an=-3+ (n - 1)9
B. a, = -1 + (n - 9)(-3)
C. an = 9+ (n-3)(-1)
D. an = 9+ (n - 1)(-3)

Answer 1

The explicit formula for the arithmetic sequence is an = -1 + (n - 1).

Step-by-step explanation:

An arithmetic sequence has a recursive formula of an = 2n - 3. To find the explicit formula for this sequence, we need to find the common difference. We can do this by subtracting the second term from the first term: (a2) - (a1) = (2(2) - 3) - (2(1) - 3) = 1. Therefore, the common difference is 1.

The explicit formula for an arithmetic sequence is an = a1 + (n - 1)∙d, where a1 is the first term and d is the common difference. So, substituting the values, we have: an = (2(1) - 3) + (n - 1)(1) = -1 + (n - 1) = A. an = -1 + (n - 1)