Question

Write an explicit formula for each geometric sequence1000,200,40,...​

Answer 1

Answer:

$\text Explicit \ Formula :\ a_{n}= 1000\times (\frac{1}{5}) ^{n-1}$

Step-by-step explanation:

Let $\left( a_{n}\right)$  be our geometric sequence

The explicit formula for $\left( a_{n}\right)$ is :

 $a_{n}= a_1\times r^{n-1}$

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:

$a_{n}= 1000\times (\frac{1}{5}) ^{n-1}$