Question

For the sequence: 8, 11, 14, 17, 20, 23, what would be the correct Slope-Intercept Explicit formula?

A) f(n)=8+3(n−1)
B) f(n)=5+3n
C) f(n) = f(n - 1) + 3, where \(f(1) = 8
D) f(n) = 8 + (n - 3), where \(f(1) = 3

Answer 1

B

Step-by-step explanation:

there is a common difference between consecutive terms in the sequence, that is

11- 8 = 14 - 11 = 17 - 14 = 20 - 17 = 23 - 20 = 3

This indicates the sequence is arithmetic with explicit formula

f(n) = a₁ +d(n - 1)

a₁ is the first term, d the common difference, n the term number

here a₁ = 8 and d = 3 , then

f(n) = 8 + 3(n - 1) = 8 + 3n - 3 = 3n + 5 = 5 + 3n

Answer 2

The correct Slope-Intercept Explicit formula for the given sequence is f(n) = 8 + 3(n-1), which corresponds to option A.

Step-by-step explanation:

The correct Slope-Intercept Explicit formula for the given sequence is f(n) = 8 + 3(n-1), which corresponds to option A.

To determine the slope-intercept form, we notice that in the given sequence, the initial term is 8 and each subsequent term increases by 3. Therefore, the common difference between consecutive terms is 3.

The formula f(n) = 8 + 3(n-1) represents this pattern, where n corresponds to the position of each term in the sequence starting from 1.