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.