Respuesta :

luisejr77

Answer:

[tex]a_{11} = 14336[/tex]

Step-by-step explanation:

The general formula for the twelfth term of a geometric sequence is:

[tex]a_n = a_1(r)^{n-1}[/tex]

Where [tex]a_1[/tex] is the first term and r is the common ratio

In this case we know that:

[tex]a_1 = 14\\r=-2[/tex]

The equation is:

[tex]a_n = 14(-2)^{n-1}[/tex]

So for [tex]n = 11[/tex] we look for [tex]a_{11}[/tex]

[tex]a_{11} = 14(-2)^{11-1}[/tex]

[tex]a_{11} = 14(-2)^{10}[/tex]

[tex]a_{11} = 14336[/tex]

alinakincsem

Answer:

[tex]11^{th}[/tex] term = 14336

Step-by-step explanation:

We are given the first term [tex] a _ 1 = 1 4 [/tex] and  common ratio [tex] r = - 2 [/tex] of a geometric sequence and we are to find the [tex]11^{th}[/tex] term of this sequence.

We know that the formula to find the [tex]n^{th}[/tex] term in a geometric sequence is given by:

[tex]n^{th}[/tex] term = [tex] a r ^ { n - 1 } [/tex]

Substituting the given values in the above formula:

[tex]11^{th}[/tex] term = [tex]14 \times(-2)^{11-1}[/tex]

[tex]11^{th}[/tex] term = [tex]14 \times(-2)^{10}[/tex]

[tex]11^{th}[/tex] term = 14336

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