Question

Write an explicit formula for each geometric sequence
1000,200,40,...​

Answer 1

`\text Explicit \ Formula :\ a_(n)= 1000* ((1)/(5)) ^(n-1)`

Explanation:

Let
`\left( a_(n)\right)` be our geometric sequence

The explicit formula for
`\left( a_(n)\right)` is :

`a_(n)= a_1* r^(n-1)`

where r is the common ratio

a1 is the first term

We notice that :

200/1000 = 1/5

40/200 = 1/5

⇒ r = 1/5

`a_1 = 1000\ \ (given)`

Conclusion:

`a_(n)= 1000* ((1)/(5)) ^(n-1)`