Question

which choice is the explicit formula for the following geometric sequence? 0.3, -0.06, 0.012, -0.0024, 0.00048

Answer 1

Answer:

$a_{n} = 0.3(- 0.2)^{n - 1}$

Step-by-step explanation:

The given sequence is 0.3, - 0.06, 0.012, - 0.0024, 0.00048 ........ so on.

Now, this is a G.P. sequence with common ratio $\frac{- 0.06}{0.3} = - 0.2$.

Now, the explicit formula of the given series will be

$a_{n} = 0.3(- 0.2)^{n - 1}$ , where $a_{n}$ is the nth term of the G.P. sequence.

Now, for n = 1, $a_{1} = 0.3(- 0.2)^{1 - 1} = 0.3$.

For, n = 2, $a_{2} = 0.3(- 0.2)^{2 - 1} = 0.3 \times (- 0.2) = - 0.06$ and so on. (Answer)