Question

Consider the sequence shown.

Answer 1

Given:

The sequence is

436, 218, 109, 54.5, 27.25,...

To find:

The explicit formula for the given sequence.

Solution:

We have,

436, 218, 109, 54.5, 27.25,...

It is a GP because the two consecutive terms have common ratio.

Here,

First term : a=436

Common ratio : d = $\dfrac{218}{436}$

                             = $\dfrac{1}{2}$

                             = $0.5$

Now, the explicit formula for a GP is

$g_n=ar^{(n-1)}$

Where, a is the first term and r is the common ratio.

Putting a=436 and r=0.5, we get

$g_n=436(0.5)^{(n-1)}$

Therefore, the correct option is c.