Question

Give a recursive definition of the sequence {an}, n = 1, 2, 3, … if

A) a1 = 1, an = an-1 + 2
B) a1 = 0, an = an-1 + 1
C) a1 = 1, an = an-1 * 2
D) a1 = 2, an = an-1 - 1

Answer 1

A recursive definition of a sequence specifies the first term and provides a rule for finding subsequent terms.

Step-by-step explanation:

A recursive definition of the sequence {an} is a definition that specifies the first term a1 in the sequence and provides a rule for finding each subsequent term in terms of previous terms.

Option A has a first term of a1 = 1, and each term after that is found by adding 2 to the previous term: an = an-1 + 2.

Option B has a first term of a1 = 0, and each term after that is found by adding 1 to the previous term: an = an-1 + 1.

Option C has a first term of a1 = 1, and each term after that is found by multiplying the previous term by 2: an = an-1 * 2.

Option D has a first term of a1 = 2, and each term after that is found by subtracting 1 from the previous term: an = an-1 - 1.