Consider the sequence shown. 436, 218, 109, 54.5, 27.25,...

Select the correct explicit formula for the sequence.

a
g_n=0.5·436^{(n-1)}

b
g_n=436·2^{(n-1)}

c
g_n=436·0.5^{(n-1)}

d
g_n=2·436^{(n-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 =

                             =

                             =

Now, the explicit formula for a GP is

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

Putting a=436 and r=0.5, we get

Therefore, the correct option is c.

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