Question

PLZ HELP THIS IS TIMED!!!!

Answer 1

Answer:

For the sequence is $-\frac{2}{3}$ ,-4 ,-24 ,-144 ,...

Hence the formula $f(x)=-\frac{2}{3}(6)^{x-1}$ for x=1,2,3,... represents the given geometric sequence

Step-by-step explanation:

Given sequence is $-\frac{2}{3}$ ,-4 ,-24 ,-144 ,...

To find the formula to describe the given sequence :

Let $a_1=\frac{-2}{3}$ ,$a_2=-4$ ,$a_3=-24$,...

First find the common ratio

$r=\frac{a_2}{a_1}$ here  $a_1=\frac{-2}{3}$ and,$a_2=-4$

$=\frac{-4}{\frac{-2}{3}}$

$=\frac{4\times 3}{2}$

$=\frac{12}{2}$

$r=6$

$r=\frac{a_3}{a_2}$ here  $a_2=-4$ and $a_3=-24$

$=\frac{-24}{-4}$

$=6$

$r=6$

Therefore the common ratio is 6

Therefore the given sequence is geometric sequence

The nth term of the geometric sequence is

$a_n=a_1r^{n-1}$

The formula which describes the given geometric sequence is

$f(x)=a_1r^{x-1}$ for x=1,2,3,...

$=\frac{-2}{3}6^{x-1}$ for x=1,2,3,...

Now verify that $f(x)=a_1r^{x-1}$ for x=1,2,3,... represents the given geometric sequence or not

put x=1 and the value of $a_1$ in $f(x)=a_1r^{x-1}$ for x=1,2,3,...

we get $f(1)=-\frac{2}{3}(6)^{1-1}$

$=-\frac{2}{3}(6)^0$

$=-\frac{2}{3}$

Therefore $f(1)=-\frac{2}{3}$

put x=2 we get $f(2)=-\frac{2}{3}(6)^{2-1}$

$=-\frac{2}{3}(6)^1$

$=-\frac{12}{3}$

Therefore $f(2)=-4$

put x=3 we get $f(3)=-\frac{2}{3}(6)^{3-1}$

$=-\frac{2}{3}(6)^2$

$=-\frac{2(36)}{3}$

Therefore $f(3)=-24$

Therefore the sequence is f(1),f(2),f(3),...

Therefore  the sequence is $-\frac{2}{3}$ ,-4 ,-24 ,-144 ,...

Hence the formula $f(x)=a_1r^{x-1}$ for x=1,2,3,... represents the given geometric sequence is verified

Therefore the formula $f(x)=-\frac{2}{3}(6)^{x-1}$ for x=1,2,3,... represents the given geometric sequence

Answer 2

Step-by-step explanation:

Answer:

For the sequence is  ,-4 ,-24 ,-144 ,...

Hence the formula  for x=1,2,3,... represents the given geometric sequence

Step-by-step explanation:

Given sequence is  ,-4 ,-24 ,-144 ,...

To find the formula to describe the given sequence :

Let  , ,,...

First find the common ratio

here   and,

here   and

Therefore the common ratio is 6

Therefore the given sequence is geometric sequence

The nth term of the geometric sequence is

The formula which describes the given geometric sequence is

for x=1,2,3,...

for x=1,2,3,...

Now verify that  for x=1,2,3,... represents the given geometric sequence or not

put x=1 and the value of  in  for x=1,2,3,...

we get

Therefore

put x=2 we get

Therefore

put x=3 we get

Therefore

Therefore the sequence is f(1),f(2),f(3),...

Therefore  the sequence is  ,-4 ,-24 ,-144 ,...

Hence the formula  for x=1,2,3,... represents the given geometric sequence is verified

Therefore the formula  for x=1,2,3,... represents the given geometric sequence