Question

20 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! A sequence {an} is defined recursively, with a1 = -1, and, for n > 1, an = an-1 + (-1)n. Find the first five terms of the sequence.

A) -1, 0, 1, 2, 3
B) -1, -2, -3, -4, -5
C) -1, 0, -1, 0, -1
D) -1, 1, -1, 1, -1

Answer 1

C.

Explanation:

Answer 2

Let's find a₂

From the recursion definition, we know that a₂ = a₁ + (-1)² = a₁ + 1 = 0

Now we know the value of a₂. Now do the same for a₃.

a₃ = a₂ + (-1)³ = a₂ - 1 = -1

So the first three term is -1, 0, -1 and C is only option that matches.

Final answer: C