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

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 = (1)/(5)`

Since,

`(125)/(625) = (1)/(5)`,

`(25)/(125) = (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 ((1)/(5))^(9)`

⇒
`a_(10) = 625 \cdot (1)/(1953125) = (1)/(3125)`

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

`a_(10) = (1)/(3125)`