Which graph represents the sequence: 1/2, 1, 2, 4,

The graph represents the sequence is Option D.

A function defined in the set of natural numbers is called a sequence.

Allow , or general term.

In a sequence, n should always represent a natural number, i.e.,

n > 0, n = 1, 2, 3, ...,

but the value of may be any real number depending on the formula for the general term of the sequence.

A sequence is considered geometric if the ratio between each consecutive term is common.  

In our problem, the sequence is

The ratio of each term to the previous term is equal 2, so we can formalize the sequence as

The consecutive terms of the sequence have a common ratio r = 2, so this sequence is geometric.

The general term of a geometric sequence with common ratio r is

Presently we go back to the question. The graph shows the horizontal axis as n and the vertical axis is the general term . The relationship between n, the terms, and the coordinates as written below:

Therefore, the graph representing the sequence is Option D.

Note:

Keywords: which, the graph, geometric sequences, common ratio, general term formula, natural numbers, The consecutive terms, arithmetic

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