Question Video: Finding the Range of an Infinite Arithmetic Sequence from Its Graph Mathematics

Find the range of the infinite arithmetic sequence represented in the figure. [A] ℝ [B] {1, 2, 3, 4, …} [C] [−8, 4] [D] {4, 0, −4, −8} [E] {4, 0, −4, −8, …}

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Video Transcript

Find the range of the infinite arithmetic sequence represented in the figure. Is it (A) the set of all real values? (B) The set of numbers one, two, three, four, and so on. (C) The values on the closed interval negative eight to four. (D) The set of numbers four, zero, negative four, negative eight. Or (E) the set of numbers four, zero, negative four, negative eight, and so on.

We are told in the question that the given sequence is arithmetic. We are also told that it is infinite, which means that the range must also be infinite. We can therefore rule out option (C) and (D) as these contain a finite set of values. The four points shown in the figure have coordinates one, four, two, zero, three, negative four, and four, negative eight. We know that the range of a function is the set of outputs or 𝑦-values. In this case, they’re equal to four, zero, negative four, and negative eight, the values of 𝑇 sub 𝑛. The range of the infinite arithmetic sequence represented in the figure is four, zero, negative four, negative eight, and so on. This means that the correct answer is option (E).

Option (B) the set of values one, two, three, four, and so on refers to the domain as this is the set of inputs or 𝑥-values. When dealing with a sequence, we know that the range must be a discrete set of values. As option (A), the set of real numbers, is continuous, we can rule out this option. This confirms that option (E) is the correct choice.

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