Question

What type of graph represents the sequence given by the explicit formula an = 5 + (n-1)2?

A) A linear graph that passes through the point (3, 0)
B) An exponential graph that passes through the point (3, 0)
C) An exponential graph that passes through the point (5, 2)
D) A linear graph that passes through the point (0, 3)

Answer 1

5 + (n - 1)²
5 + (n - 1)(n - 1)
5 + (n² - n - n + 1)
5 + (n² - 2n + 1)
n² - 2n + 1 + 5
n² - 2n + 6 = 0
n = -(-2) +/- √((-2)² - 4(1)(6))
2(1)
n = 2 +/- √(4 - 24)
2
n = 2 +/- √(-20)
2
n = 2 +/- 2i√(5)
2
n = 1 + i√(5)
n = 1 + i√(5) n = 1 - i√(5)

The answer is equal to B.