Answer:
The 8th term of the following sequence is 9375.
Step-by-step explanation:
Given the sequence
3/25, 3/5, 3, 15
As we know that a geometric sequence has a constant ratio and is defined by:
[tex]\:a_n=a_0\cdot r^{n-1}[/tex]
so
[tex]\frac{3}{25},\:\frac{3}{5},\:3,\:15[/tex]
[tex]\frac{\frac{3}{5}}{\frac{3}{25}}=5,\:\quad \frac{3}{\frac{3}{5}}=5,\:\quad \frac{15}{3}=5[/tex]
As the ratio 'r' is the same.
so
[tex]r=5[/tex]
As the first element of the sequence is
[tex]a_1=\frac{3}{25}[/tex]
Therefore, the nth term is computed by
[tex]\:a_n=a_0\cdot r^{n-1}[/tex]
[tex]a_n=\frac{3}{25}\cdot \:5^{n-1}[/tex]
Putting n = 8 to determine the 8th term.
[tex]a_8=5^7\cdot \frac{3}{25}[/tex]
[tex]a_8=\frac{3\cdot \:5^7}{25}[/tex]
[tex]=\frac{5^7\cdot \:3}{5^2}[/tex]
[tex]=5^5\cdot \:3[/tex]
[tex]=9375[/tex]
Therefore, the 8th term of the following sequence is 9375.
