Question

Write the explicit formula for the geometric sequence.

Answer 1

Answer:

It is D

Step-by-step explanation:

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Answer 2

Answer:

Option D is correct.

Explicit formula for the geometric sequence is, $a_n = 64 \cdot (0.5)^{n-1}$

Step-by-step explanation:

Geometric sequence states that a sequence of numbers in which the ratio between consecutive terms is constant,

we can write a formula for the nth geometric sequence in the form of:

$a_n = a_1r^{n-1}$ .....[1] where $a_1$ is the first term and  r is the common ratio between successive term.

Given the sequence: 64, 32, 16 , 8......

Here, first term ($a_1$) = 64.

Common ratio(r) = 0.5

Since,

$\frac{32}{64} =0.5$

$\frac{16}{32} = 0.5$ ,

$\frac{8}{16} = 0.5$ ......

Substitute the value of a and r in [1] we get;

$a_n = 64 \cdot (0.5)^{n-1}$

therefore, the explicit formula for the geometric sequence is, $a_n = 64 \cdot (0.5)^{n-1}$