Mathematics: Identify a1 and r for the geometric sequence an= -256(-1/4) n-1

Identify a1 and r for the geometric sequence an=

Ответ:

Learsyguerra26

09.03.2022

Mathematics

The value of the term a_1 is -256 and r is -1/4.

What is the geometric sequence?

In a Geometric Sequence, each term is found by multiplying the previous term by a constant.

The standard formula for finding the nth term of the geometric sequence is;

$\rm a_n = a_1 \times r^{n-1}$

Where a1 is the first term and r is the common ratio.

The formula for finding the nth term of the geometric sequence is;

$\rm a_n= -256\dfrac{-1}{4}^{(n-1)}\\\\$

The first term of the sequence is;

$\rm a_n= -256\dfrac{-1}{4}^{(n-1)}\\\\ n=1\\\\ \rm a_n= -256\dfrac{-1}{4}^{(1-1)}\\\\ a_n=-256$

The second term of the sequence is;

$\rm a_n= -256\dfrac{-1}{4}^{(n-1)}\\\\ n=1\\\\ \rm a_n= -256\dfrac{-1}{4}^{(2-1)}\\\\ a_n=64$

Therefore,

The value of r is;

$\rm r=\dfrac{a_2}{a_1}\\\\r=\dfrac{64}{-256}\\\\r= \dfrac{-1}{4}$

Hence, the value of the term a_1 is -256 and r is -1/4.

To know more about Geometric progression click the link given below.

link

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Ответ:

ayoismeisalex

09.03.2022

Mathematics

a_1=-256

$r=-\frac{1}{4}$

Step-by-step explanation:

The geometric sequence is given by :-

a,ar,ar^2,ar^3,..... , where a is the first term and r is the constant ratio.

The given explicit formula of nth term :- $a_n=-256(-\frac{1}{4})^{n-1}$

First term= $a_1=-256(-\frac{1}{4})^{1-1}=-256(1)=-256$

Hence, a_1=-256

Second term = $a_2=-256(\frac{1}{4})^{2-1}=-256(-\frac{1}{4})=64$

Now, $r=\frac{a_2}{a_1}=\frac{64}{-256}=-\frac{1}{4}$

hence, $r=-\frac{1}{4}$

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Ответ:

popa60

01.05.2020

Mathematics

Ain’t nobody know the answer

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Identify a1 and r for the geometric sequence an= -256(-1/4) n-1

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