Question

The function q(n) = 2n^2 - 8n and five consecutive integer values of n determine the following sequence:

-6, 0, ___, 24, 42
Which of the following provides the missing value in the sequence?
a) 12
b) 18
c) 6
d) 36

Answer 1

The missing value in the sequence generated by the function q(n) = 2n² - 8n, given the terms -6, 0, ___, 24, 42, is 18.

Step-by-step explanation:

To find the missing value in the sequence derived from the function q(n) = 2n² - 8n, we notice that the sequence is generated by plugging in consecutive integer values of n. Looking at the given sequence (-6, 0, ___, 24, 42), we can infer that each term in the sequence corresponds to subsequent integer values of n. Since -6 to 0 is an increment of 6, and 0 to 24 is an increment of 24, it implies jumps in increments of 6, 12, 18, and so on, which are differences between consecutive squares multiplied by 2, according to the function q(n). Therefore, to find the missing number (where the increment should be 18), we add 18 to 0 and get 18 as the missing term.