How do you write the first five terms of the geometric sequence $a_{1} = 1, r = \frac{1}{2}$ $a_1=1, r=1/2$ ?

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How do you write the first five terms of the geometric sequence $a_{1} = 1, r = \frac{1}{2}$ $a_1=1, r=1/2$ ?

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Answer 1 · 2017-07-26T17:14:42

$1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}$ $1, 1/2,1/4,1/8,1/16$

Explanation:

Geometric sequences are defined by the formula $a r^{n - 1}$ $ar^(n-1)$ where $a$ $a$ is the first term and $r$ $r$ is the common ratio (i.e. the second term divided by the first term or third divided by second).

When $n = 1$ $n=1$ , $a r^{n - 1}$ $ar^(n-1)$ becomes $1 \times {(\frac{1}{2})}^{1 - 1} = 1 \times 1$ $1times(1/2)^(1-1)=1times1$ (anything to the power of zero is one).

When $n = 2$ $n=2$ , $a r^{n - 1}$ $ar^(n-1)$ becomes $1 \times {(\frac{1}{2})}^{2 - 1} = 1 \times \frac{1}{2}$ $1times(1/2)^(2-1)=1times1/2$ and so on.

Answer 2 · 2017-07-26T19:20:37

$1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}$ $1,1/2,1/4,1/8,1/16$

Explanation:

$the standard terms of a geometric sequence are$ $"the standard terms of a geometric sequence are"$

$a,ar,ar^2,ar^3,........ ,ar^(n-1)$

$"where a is the first term and r the common ratio"$

$"to obtain a term in the sequence multiply the previous"$
$"term by r"$

$"here "a=a_1=1" and "r=1/2$

$a_1=1$

$a_2=1xx1/2=1/2$

$a_3=1/2xx1/2=1/4$

$a_4=1/4xx1/2=1/8$

$a_5=1/8xx1/2=1/16$

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How do you write the first five terms of the geometric sequence $a_{1} = 1, r = \frac{1}{2}$ $a_1=1, r=1/2$ ?

2 Answers

Explanation:

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How do you write the first five terms of the geometric sequence a_1=1, r=1/2a1=1,r=12a_1=1, r=1/2?

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How do you write the first five terms of the geometric sequence $a_{1} = 1, r = \frac{1}{2}$ $a_1=1, r=1/2$ ?