Question

Create an equation to represent the sequence: 1000,100,10,1,0.1,

Answer 1

Geometric Sequences

In geometric sequences, each term can be obtained by multiplying the previous term by a fixed number, called 'common ratio'

Please note the first term is 1000 and the second is 1000/10 = 100.

The third term is 100/10=10.

The rule is: 'divide the previous term by 10 to get the next term'

The general formula for a geometric series is:

`a_n=a_1\cdot r^{\mleft\{n-1\mright\}}`

Where an is the term n, a1 is the first term, and r is the common ratio.

From the sequence, we can know the required values:

a1=1000

r = 1/10 = 0.1

Thus the general term is expressed with the following equation:

`a_n=1000\cdot0.1^{\{n-1\}}`

Let's test for n=2 (the second term):

`a_2=1000\cdot0.1^{\{2-1\}}=1000\cdot0.1=100`

The equation is accurate for any value of n, thus the answer is:

`a_n=1000\cdot0.1^{\{n-1\}}`