To show that arithmetic sequence formulas have the same structure as linear function, choose the linear function equation that has the same structure as the arithmetic sequence A n = 6 + (n - 1) x 8.
A. y = 6x + 8
B. y = 8x + 6
C. y = 8x - 2
D. y = 2x - 8
The answer is B. y = 8x + 6.
To see why, let's break down the given arithmetic sequence formula:
Aₙ = 6 + (n - 1) × 8
In this formula:
- Aₙ represents the nth term of the arithmetic sequence.
- 6 is the first term of the sequence.
- (n - 1) represents the number of terms that have been added to the first term, starting from 1.
- 8 is the common difference between terms.
Now let's compare this to the linear function equation options:
A. y = 6x + 8
B. y = 8x + 6
C. y = 8x - 2
D. y = 2x - 8
Looking at option B, we can see that it matches the structure of the arithmetic sequence formula:
- The constant term 6 in the arithmetic sequence formula corresponds to the constant term 6 in the linear function equation.
- The coefficient (n - 1) of the common difference in the arithmetic sequence formula corresponds to the coefficient 8 of the linear function equation.
- The variable n in the arithmetic sequence formula corresponds to the variable x in the linear function equation.
Therefore, option B. y = 8x + 6 has the same structure as the arithmetic sequence formula given.