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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)=(-6) f(n − 1) +11

The first 4 terms of the sequence are _______, _______, _______, and _______.

A. 8, 2, -4, 14
B. 8, 2, 14, -4
C. 8, -4, 2, 14
D. 8, 14, 2, -4

User Dork
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1 Answer

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Final answer:

The first four terms of the sequence, calculated using the recursive function f(n)=(-6) f(n - 1) + 11, are 8, -37, 233, and -1387. These results do not match the provided choices, indicating a possible error in the options.

Step-by-step explanation:

The question asks us to find the first 4 terms of the sequence defined by a recursive function. To find each term, we use the previous term in the sequence, apply the given rule, and calculate the next value. We begin with the given first term, f(1) = 8. The rule is f(n)=(-6) f(n − 1) + 11, which means that each term is negative six times the previous term plus eleven.

  • f(2)=(-6)×f(1)+11 = (-6)×(8)+11 = -48 + 11 = -37
  • f(3)=(-6)×f(2)+11 = (-6)×(-37)+11 = 222 + 11 = 233
  • f(4)=(-6)×f(3)+11 = (-6)×(233)+11 = -1398 + 11 = -1387

Therefore, the first four terms of the sequence are 8, -37, 233, and -1387. These results do not match any of the options (A, B, C, or D) as listed in the question, implying that there may be an error in the options provided. The correct answer must reflect the recursive calculation as per the given rule.

User Stealthcopter
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