contestada

5. A state began an effort to increase the
deer population. In year 2 of the ef-
fort, the deer population in a state
forest was 2,400. In year 4, the pop-
ulation was 3,456. Write an explicit
rule for the sequence using subscript
notation.

Respuesta :

varshamittal029

The explicit rule for the sequence using subscript notation is [tex]a_n=2000\times1.2^{n-1}[/tex] .

  • Explicit expressions are always used to represent any term in a sequence without describing any other term in the sequence. The meaning of "explicit" is direct, something that can be found directly  without knowing the other terms in the sequence.
  • A term in a sequence can be uniquely represented by a single expression, an explicit expression.
  • Geometric Sequence: [tex]a_n=ar^{n-1}[/tex], where 'a' is the first term and 'r' is the common ratio.

It is given that sequence is G.P

In G.P 2nd and 4th is given by

 [tex]a_2=ar[/tex]      ...(1)      and              [tex]a_4=ar^3[/tex]  ...(2)

We have given [tex]a_2=2400 , a_4=3456[/tex]

Putting in equation (1) and (2) , we get

       [tex]2400=ar[/tex]    ...(3)          and           [tex]3456=ar^3[/tex]      ...(4)

On dividing equation (3) by equation (4) , we get

        [tex]\frac{2400}{3456} =\frac{ar}{ar^3} \\\\\\ 0.6944=\frac{1}{r^2}\\\\r^2=1.44 \\r=1.2[/tex]

First term will be given by

       [tex]a_1=a_2 r^{1-2}\\\\a_1=2400r^{-1}\\\\a_1=\frac{2400}{1.2} \\\\a_1=2000[/tex]

Nth term is given by

[tex]a_n=a_1r^{n-1}\\a_n=2000\times1.2^{n-1}[/tex]

Learn more about sequence here :

https://brainly.com/question/17615101

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