Question

An arithmetic sequence has this recursive formula:(a₁ = 5an = an-1-4What is the explicit formula for this sequence?O A. an=5+ (n − 1)(-4)OB. an=5+ (n −4)(-1)OC. an= (-4) + (n-1)5O D. an= (-1) + (n - 5)(-4)

Answer 1

Answer:

A. an = 5 + (n - 1)(-4)

Explanation:

The explicit formula of an arithmetic sequence has the form

an = a1 + (n-1)d

Where a1 is the first term and d is a common difference.

Now, the recursive formula is

a1 = 5

an = a(n-1) - 4

So, we know that a1 = 4 and d = -4 because the common difference is the difference between two consecutive values.

Then, the explicit formula is

an = 5 + (n - 1)(-4)

So, the answer is A