Respuesta :
Answer:
The 6th term of the sequence is 0.125.
Step-by-step explanation:
Given : Geometric Sequence where[tex]a_1=128[/tex] and [tex]a_3=8[/tex]
To find : The 6th term.
Solution :
The formula of nth term of geometric sequence is
[tex]a_n=a_1\times r^{n-1}[/tex] ........[1]
We have given,
[tex]a_1=128[/tex]
[tex]a_3=8[/tex]
To find ratio we put n=3 in [1]
[tex]a_3=a_1\times r^{3-1}[/tex]
[tex]8=128\times r^{2}[/tex]
[tex]\frac{8}{128}= r^{2}[/tex]
[tex]0.0625= r^{2}[/tex]
[tex]r=\sqrt{0.0625}[/tex]
[tex]r=0.25[/tex]
Now, we know first term [tex]a_1=128[/tex] and common ratio [tex]r=0.25[/tex]
Put n=6 in [1] to get 6th term of the sequence is
[tex]a_6=a_1\times r^{6-1}[/tex]
[tex]a_6=128\times (0.25)^{5}[/tex]
[tex]a_6=128\times 0.000976[/tex]
[tex]a_6=0.125[/tex]
Therefore, The 6th term of the sequence is 0.125.
