Respuesta :
Answer: [tex]a_1=-256[/tex]
[tex]r=-\frac{1}{4}[/tex]
Step-by-step explanation:
The geometric sequence is given by :-
[tex]a,ar,ar^2,ar^3,.....[/tex], where a is the first term and r is the constant ratio.
The given explicit formula of nth term :-[tex]a_n=-256(-\frac{1}{4})^{n-1}[/tex]
First term=[tex]a_1=-256(-\frac{1}{4})^{1-1}=-256(1)=-256[/tex]
Hence, [tex]a_1=-256[/tex]
Second term = [tex]a_2=-256(\frac{1}{4})^{2-1}=-256(-\frac{1}{4})=64[/tex]
Now, [tex]r=\frac{a_2}{a_1}=\frac{64}{-256}=-\frac{1}{4}[/tex]
hence, [tex]r=-\frac{1}{4}[/tex]
The value of the term [tex]a_1[/tex] 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;
[tex]\rm a_n = a_1 \times r^{n-1}[/tex]
Where a1 is the first term and r is the common ratio.
The formula for finding the nth term of the geometric sequence is;
[tex]\rm a_n= -256\dfrac{-1}{4}^{(n-1)}\\\\[/tex]
The first term of the sequence is;
[tex]\rm a_n= -256\dfrac{-1}{4}^{(n-1)}\\\\ n=1\\\\ \rm a_n= -256\dfrac{-1}{4}^{(1-1)}\\\\ a_n=-256[/tex]
The second term of the sequence is;
[tex]\rm a_n= -256\dfrac{-1}{4}^{(n-1)}\\\\ n=1\\\\ \rm a_n= -256\dfrac{-1}{4}^{(2-1)}\\\\ a_n=64[/tex]
Therefore,
The value of r is;
[tex]\rm r=\dfrac{a_2}{a_1}\\\\r=\dfrac{64}{-256}\\\\r= \dfrac{-1}{4}[/tex]
Hence, the value of the term [tex]a_1[/tex] is -256 and r is -1/4.
To know more about Geometric progression click the link given below.
https://brainly.com/question/12115906
