Question

What is the 8th term of the following sequence? 3/25, 3/5, 3, 5

Answer 1

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:

$\:a_n=a_0\cdot r^{n-1}$

so

$\frac{3}{25},\:\frac{3}{5},\:3,\:15$

$\frac{\frac{3}{5}}{\frac{3}{25}}=5,\:\quad \frac{3}{\frac{3}{5}}=5,\:\quad \frac{15}{3}=5$

As the ratio 'r' is the same.

so

$r=5$

As the first element of the sequence is

$a_1=\frac{3}{25}$

Therefore, the nth term is computed by

$\:a_n=a_0\cdot r^{n-1}$

$a_n=\frac{3}{25}\cdot \:5^{n-1}$

Putting n = 8 to determine the 8th term.

$a_8=5^7\cdot \frac{3}{25}$

$a_8=\frac{3\cdot \:5^7}{25}$

    $=\frac{5^7\cdot \:3}{5^2}$

     $=5^5\cdot \:3$

     $=9375$

     

Therefore, the 8th term of the following sequence is 9375.