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My name is Ann [436]
3 years ago
9

Which graph represents the sequence: 1/2, 1, 2, 4, 8...?

Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
6 0

The graph represents the sequence is Option D.

<h3>Further explanation </h3>

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

Allow \boxed{a_n \ as \ n^{th} \ term}, 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 \boxed{a_n} 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 \boxed{ \ \frac{1}{2}, 1, 2, 4, 8, ... \ }

The ratio of each term \boxed{a_{n+1}} to the previous term \boxed{a_n} is equal 2, so we can formalize the sequence as

\boxed{\frac{a_{n+1}}{a_n} =2}.

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

The general term of a geometric sequence \boxed{a_n} with common ratio r is \boxed{\boxed{ \ a_n = a_1 \cdot r^{n-1} \ }}.

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

\boxed{n = 1 \rightarrow the \ 1st \ term \ a_1 = \frac{1}{2} \rightarrow \bigg( 1, \frac{1}{2} \bigg)}

\boxed{n = 2 \rightarrow the \ 2nd \ term \ a_2 = 1 \rightarrow (2, 1)}

\boxed{n = 3 \rightarrow the \ 3rd \ term \ a_3 = 2 \rightarrow (3, 2)}

\boxed{n = 4 \rightarrow the \ 4th \ term \ a_4 = 4 \rightarrow (4, 4)}

\boxed{n = 5 \rightarrow the \ 5th \ term \ a_5 = 8 \rightarrow (5, 8)}

Therefore, the graph representing the sequence is Option D.

<u>Note:</u>

  • The general term of a geometric sequence is exponential.
  • From the common ratio (r > 1) and graph, the type is an increasing sequence.
<h3>Learn more </h3>
  1. Combining two functions to create a geometric sequence brainly.com/question/1695742
  2. A word problem about arithmetic and geometric sequences brainly.com/question/3395975
  3. Drawing graph of the geometric sequence brainly.com/question/3166290

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

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