Question

For each positive integer n, the nth term of the sequence s is 1 (-1)ⁿ.

a) s₁ = -1
b) s₂ = 1
c) s₃ = -1
d) s₄ = 1

Answer 1

The nth term of the sequence s is given by 1*(-1)^n. For s1, s2, s3, and s4, the values correspondingly are -1, 1, -1, and 1, demonstrating an alternating pattern due to the exponent n.

Step-by-step explanation:

The question asks to determine the values of a sequence s defined by its nth term as 1*(-1)^n for each positive integer n. For each term of the sequence, we follow the definition to get:

• For s1, n=1, which gives us 1*(-1)1 = -1.
• For s2, n=2, which gives us 1*(-1)2 = 1.
• For s3, n=3, which gives us 1*(-1)3 = -1.
• For s4, n=4, which gives us 1*(-1)4 = 1.

This pattern of alternating signs is due to the exponent n being an integer that determines whether the term is negative or positive, which alternates with every increase in n.