Help pleaseeeeee A. Write a recursive formula for the sequence. 6, 17, 28, 39, 50, ... A. f(1) = 6; f(n) = f(n-1) + 11 B. f(1) = 6; f(n) = 6 f(n-1) + 11 C. f(1) = 6; f(n) = f(n-1) + 6 D. f(1) = 6; f(n) = 11 f(n-1)
Mathematics · College · Tue Nov 03 2020
Answered on
Given the sequence:
6, 17, 28, 39, 50,
Determine the recursive formula.
Solution:
In order to determine the recursive formula of the given arithmetic sequence, we must first take note of its common difference since it is not yet given. To find for the common difference, we must subtract the second term by the first term.
First term = 6
Second term = 17
Common Difference = Second term - First term
Common Difference = 17 - 6
Common Difference = 11
The given choices do not have a correct answer, since,
A. f(1) = 6; f(n) = f(n-1) + 11
The first term should be included.
B. f(1) = 6; f(n) = 6 f(n-1) + 11
The first term is not multiplied with f(n-1), it should be 11, and their product must be added by the first term.
C. f(1) = 6; f(n) = f(n-1) + 6
The common difference should be included.
D. f(1) = 6; f(n) = 11 f(n-1)
The first term should be included.
To determine the correct answer, we refer to the formula for arithmetic sequence.
F(n) = A1 + f(n-1)d
F(n) = 6 + f(n-1)11
Final answer:
F(n) = 6 + f(n-1)11