Respuesta :

Answer:  Option 'c' is correct.

Step-by-step explanation:

Since we have given that

16,24,36,54.....

Since it is a geometric sequence.

Here, a = first term = 16

r = common ratio is given by

[tex]\frac{a_2}{a_1}=\frac{24}{16}=\frac{3}{2}[/tex]

So, n th term ( explicit form ) will be

[tex]a_n=16(\frac{3}{2})^{n-1}[/tex]

Hence, Option 'c' is correct.

abidemiokin

The explicit  form of the function that describes the sequence below is [tex]T_n=16(3/2)^{n-1}[/tex]

Explicit function of a sequence

The geometric sequence are sequence that increases exponentially. Given the geometric sequence, the nth term of the sequence is expressed as:

[tex]T_n=ar^{n-1}[/tex]

where

  • a is the first term
  • n is the number of terms
  • r is the common ratio

Given the following

a = 16

r =24/16  = 1.5

Substitute

[tex]T_n=16(3/2)^{n-1}[/tex]

Hence the explicit  form of the function that describes the sequence below is [tex]T_n=16(3/2)^{n-1}[/tex]

Learn more on geometric sequence here: https://brainly.com/question/24643676

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