Question

Enter the first 4 terms of the sequence defined by the given rule. Assume that the domain of each function is the set of whole numbers greater than 0.

f(1) = 8, f(n) = (-3) * f(n - 1) + 14
A) 8, -10, 24, -30
B) 8, -6, 2, -10
C) 8, 4, -2, -6
D) 8, 14, 20, 26

Answer 1

The first four terms of the sequence defined by f(1) = 8 and f(n) = (-3) × f(n - 1) + 14 are 8, -10, 44, and -118.

Step-by-step explanation:

The sequence given by f(1) = 8, f(n) = (-3) × f(n - 1) + 14 can be determined step-by-step for the first four terms. To find each term, we use the previous term substituted in the given function rule.

• First term: f(1) = 8
• Second term: f(2) = (-3) × f(1) + 14 = (-3) × 8 + 14 = -24 + 14 = -10
• Third term: f(3) = (-3) × f(2) + 14 = (-3) × (-10) + 14 = 30 + 14 = 44
• Fourth term: f(4) = (-3) × f(3) + 14 = (-3) × 44 + 14 = -132 + 14 = -118

Therefore, the first four terms of the sequence are 8, -10, 44, -118.