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2 years ago

Write an equation for the nth term of the geometric sequence: 4, 8, 16 . . .

Mathematics

1 answer:

kogti [31]2 years ago

7 0

nth term for the geometric sequence 4,8,16,... is $a_n=4(2)^{n-1}$

Step-by-step explanation:

We need to write an equation for the nth term of the geometric sequence: 4, 8, 16 . . .

The formula to find the nth term of geometric sequence is

$a_n=a_1r^{n-1}$

Where a_n is nth term

a_1 is 1st term

and r is common ratio

Finding a_1 and r in the sequence 4,8,16,...

$a_1=4\\r=\frac{a_2}{a_1}\\r=\frac{8}{4}\\r=2$

So, common ratio r is: 2 and a_1 is 4

The nth term is:

$a_n=4(2)^{n-1}$

So, nth term for the geometric sequence 4,8,16,... is $a_n=4(2)^{n-1}$

Keywords: Geometric sequence

Learn more about Geometric sequence at:

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Which sum does not equal ?<br> 7/8

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The sum which is not equal to 7/8 is 7/8 +7/8 = 14/8

Given,

a) 2/8 + 5/8 = 7/8 which is equal to 7/8.

Therefore, option a) is incorrect.

b) 1/8 + 6/8 = 7/8, which is also equal to 7/8.

Option b) is also incorrect.

c) 7/8 + 7/8 = 14/8 , which is not equal to 7/8.

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Option d) is also incorrect.

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Given f of x is equal to the quantity x minus 4 end quantity divided by the quantity x squared plus 13x plus 36 end quantity, wh

gavmur [86]

The simplified expression of the function $f(x) =\dfrac{x-4}{x^2+13x+36}$ is

$f(x) = \dfrac{x-4}{(x+9)(x+4)}$ . f(x) is increasing for all x > –4.The correct answer is option C.

<h3>What is a function?</h3>

A function is defined as a relation between the set of inputs having exactly one output each.

The function expression is given as:

$f(x) =\dfrac{x-4}{x^2+13x+36}$

Expand the denominator

$f(x) =\dfrac{x-4}{x^2+4x +9x+36}$

Factorize the denominator

$f(x) =\dfrac{x-4}{x(x+4)+9(x+4)}$

Factor out x + 9

$f(x) = \dfrac{x-4}{(x+9)(x+4)}$

The simplified expression of the function $f(x) =\dfrac{x-4}{x^2+13x+36}$ is

$f(x) = \dfrac{x-4}{(x+9)(x+4)}$ . f(x) is increasing for all x > –4

Write an equation for the nth term of the geometric sequence: 4, 8, 16 . . .​

Write an equation for the nth term of the geometric sequence: 4, 8, 16 . . .