Answer:
The 8th term of the geometric sequence 5, -15, 45, ... is:
[tex]a_8=-10935[/tex]
Step-by-step explanation:
Given the geometric sequence
5, -15, 45, ...
The first element of the geometric sequence is
[tex]a_1=5[/tex]
A geometric sequence has a constant ratio 'r' and is defined by
[tex]a_n=a_1\cdot r^{n-1}[/tex]
computing the ratios of all the adjacent terms
[tex]\frac{-15}{5}=-3,\:\quad \frac{45}{-15}=-3[/tex]
The ratio between all the adjacent terms is the same and equal to
[tex]r=-3[/tex]
substituting [tex]a_1=5[/tex], and [tex]r=-3[/tex] in the nth term
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]a_n=5\left(-3\right)^{n-1}[/tex]
Determining the 8th term:
We have already got the nth term
[tex]a_n=5\left(-3\right)^{n-1}[/tex]
substituting n = 8 to determine the 8th term
[tex]a_n=5\left(-3\right)^{n-1}[/tex]
[tex]a_8=5\left(-3\right)^{8-1}[/tex]
[tex]a_8=5\left(-3^7\right)[/tex]
[tex]a_8=-5\cdot \:3^7[/tex]
[tex]a_8=-5\cdot \:2187[/tex]
[tex]a_8=-10935[/tex]
Therefore, the 8th term of the geometric sequence 5, -15, 45, ... is:
[tex]a_8=-10935[/tex]
