Question

What type of graph represents the sequence given by the explicit formula an = 5 + (n-1)2? 1) A) A linear graph that passes through the point (3, 0) 2) B) An exponential graph that passes through the point (3, 0) 3) C) An exponential graph that passes through the point (5, 2) 4) D) A linear graph that passes through the point (0, 3)

Answer 1

The sequence given by the explicit formula an = 5 + (n-1)2 is represented by a linear graph that passes through the point (3, 0).

Step-by-step explanation:

The sequence given by the explicit formula an = 5 + (n-1)2 is represented by a linear graph that passes through the point (3, 0).

To determine this, we can simplify the equation by expanding the brackets and rearranging: an = 5 + 2n - 2.

The resulting equation, y = 2n + 3, is in the form y = mx + b, where m is the slope and b is the y-intercept. Since the slope is non-zero and positive, the graph represents a linear relationship. Furthermore, the point (3, 0) lies on this line, confirming that it is the correct graph representation.

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