ystyrixkzd

2023-03-31

Write formula for the sequence of -4, 0, 8, 20, 36, 56, 80, where the order of f(x) is 0, 1, 2, 3, 4, 5, 6 respectively

coguarsbq2q

To find a formula for the given sequence {-4, 0, 8, 20, 36, 56, 80} with corresponding values of f(x) = {0, 1, 2, 3, 4, 5, 6}, we can try to identify a pattern and establish a relationship between the terms.
By examining the sequence, we can observe that the difference between consecutive terms increases by 4 each time. Additionally, the value of f(x) corresponds to the index of each term minus 1.
Based on these observations, we can propose a formula for the sequence. Let's call the index of the term n (starting from 0), so the corresponding f(x) would be n - 1. The formula can be written as:
Term(n) = (n - 1) * (n - 1) * 4 - 4
Substituting the values of f(x) into the formula, we have:
Term(0) = (0 - 1) * (0 - 1) * 4 - 4 = -4
Term(1) = (1 - 1) * (1 - 1) * 4 - 4 = 0
Term(2) = (2 - 1) * (2 - 1) * 4 - 4 = 8
Term(3) = (3 - 1) * (3 - 1) * 4 - 4 = 20
Term(4) = (4 - 1) * (4 - 1) * 4 - 4 = 36
Term(5) = (5 - 1) * (5 - 1) * 4 - 4 = 56
Term(6) = (6 - 1) * (6 - 1) * 4 - 4 = 80
Therefore, the proposed formula, Term(n) = (n - 1) * (n - 1) * 4 - 4, matches the given sequence with corresponding f(x) values.

Bollacasaep22

We can observe that the difference between consecutive terms increases by 4 each time. Moreover, the value of f(x) corresponds to the index of each term.
Based on these observations, we can propose a revised formula for the sequence. Let's call the index of the term n, and the corresponding f(x) value would be n. The formula can be written as:
Term(n) = n^2 * 4 - 4
Substituting the values of f(x) into the formula, we have:
Term(0) = 0^2 * 4 - 4 = -4
Term(1) = 1^2 * 4 - 4 = 0
Term(2) = 2^2 * 4 - 4 = 8
Term(3) = 3^2 * 4 - 4 = 20
Term(4) = 4^2 * 4 - 4 = 36
Term(5) = 5^2 * 4 - 4 = 56
Term(6) = 6^2 * 4 - 4 = 80
Therefore, the revised formula, Term(n) = n^2 * 4 - 4, matches the given sequence with corresponding f(x) values.

Do you have a similar question?