Question

What is the 10th term of the sequence 625,125 25,...?

Answer 1

1 = 625
2 = 125
3 = 25
4 = 5
5 = 1
6 = 1/5
7 = 1/25
8 = 1/125
9 = 1/625
10 = 1/3125

Answer 2

Answer:

The nth term for the geometric sequence is given by:

$a_n=a_1r^{n-1}$                  .......[1]

where,

$a_1$ is the first term

r is the common ratio of two consecutive terms

n is the number of terms.

Given the sequence:

625,125 25,...

This is a geometric sequence with first term($a_1$) = 625

and $r = \frac{1}{5}$

Since,

$\frac{125}{625} = \frac{1}{5}$,

$\frac{25}{125} = \frac{1}{5}$ and so on...

We have to find the 10th term of the given sequence

For n = 10

Substitute the given values in [1] we have;

$a_{10} = 625 \cdot (\frac{1}{5})^{9}$

⇒$a_{10} = 625 \cdot \frac{1}{1953125} = \frac{1}{3125}$

Therefore, the 10th term of the given sequence  is,

$a_{10} = \frac{1}{3125}$