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3 years ago

A geometric sequence is defined by the equation an = (4)3 − n. What are the first three terms of the sequence and what is the co

mmon ratio, r?

Mathematics

1 answer:

grigory [225]3 years ago

4 0

$x_{n} = 4^{3-n} , x_{1} =4^{3-1}=4^{2}=16

x_{2}=4^{3-2}=4^{1}=4

x_{3}= 4^{3-3}= 4^{0} =1

Common ratio = x_{3}/x_{2}= \frac{1}{4}$

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The graph of the function g(x)= x^2+3x-4 is shifted 5 units to the left

omeli [17]

<h3>THE MID TERM SPLITTING OF THE EQUATION IS :</h3>

${x}^{2} + 3x - 4$

${x}^{2} + 4x - x - 4$

$x(x + 4) - 1(x + 4)$

$x = -4 \: and \: 1$

$x = 1$

now shifted to 5 units left

therefore,

x=-4

hope it helps you mate thanks for the question and if possible please mark it as brainliest

5 0

3 years ago

Write a recursive rule for the sequence.

Vadim26 [7]

Answer:

f(n)=f(n-1)+f(n-2)

f(1)=1x

f(2)=1x

Step-by-step explanation:

This is the fibonacci sequence with each term times x.

Notice, you are adding the previous two terms to get the third term per consecutive triples of the sequence.

That is:

1x+1x=2x

1x+2x=3x

2x+3x=5x

3x+5x=8x

So since we need the two terms before the third per each consecutive triple in the sequence, our recursive definition must include two terms of the sequence. People normally go with the first two.

f(1)=1x since first term of f is 1x

f(2)=1x since second term of f is 1x

Yes, I'm naming the sequence f.

So I said a third term in a consecutive triple of the sequence is equal to the sum of it's two prior terms. Example, f(3)=f(2)+f(1) and f(4)=f(3)+f(2) and so on...

Note, the term before the nth term is the (n-1)th term and the term before the (n-1)th term is the (n-2)th term. Just like before the 15th term you have the (15-1)th term and before that one you have the (15-2)th term. That example simplified means before the 15th term you have the 14th and then the 13th.

So in general f(n)=f(n-1)+f(n-2).

So the full recursive definition is:

f(n)=f(n-1)+f(n-2)

f(1)=1x

f(2)=1x

8 0

3 years ago

Simplify the rational expression. State any restrictions on the variable.

ExtremeBDS [4]

we are given

$\frac{(n^4-10n^2+24)}{(n^4-9n^2+18)}$

Firstly, we will factor numerators and denominators

$\frac{(n^4-10n^2+24)}{(n^4-9n^2+18)}=\frac{(n^2-6)(n^2-4)}{(n^2-3)(n^2-6)}$

we can see that

n^2 -6 is factor on both numerator and denominator

so, it will get cancelled

and n^2 -6 can not be equal to 0

so, one of restriction is

$n^2-6\neq 0$

$n\neq -+ \sqrt{6}$

we can simplify it

$\frac{(n^4-10n^2+24)}{(n^4-9n^2+18)}=\frac{(n^2-4)}{(n^2-3)}$

we know that denominator can not be zero

$n^2-3\neq 0$

$n\neq -+ \sqrt{3}$

so, option-B.......Answer

3 0

3 years ago

How many dots are in the 4th step?

Mkey [24]

Answer:

Step-by-step explanation:

if you look at the diagram the dot goes up 1 each. It also makes another row which makes 4 rows total. Since 3 contains 7 dots and 3 rows we would do 8 in 4 rows. 8 x 4 is 32.

Hope this helped!

7 0

3 years ago

Read 2 more answers

Which number can each term of the equation be multiplied by to eliminate the decimals before solving?

Sati [7]

Ok...

5.6 = 56/10 = 560/100

1.1 = 11/10 = 110/100

0.12 = 12/100

--------------

$\frac { 560 }{ 100 } j-\frac { 12 }{ 100 } =4+\frac { 110 }{ 100 } j\\ \\ \\ 100\times \left( \frac { 560 }{ 100 } j-\frac { 12 }{ 100 } \right) =\left( 4+\frac { 110 }{ 100 } j \right) \times 100\\ \\ 560j-12=400+110j\\ \\ 560j-110j=400+12\\ \\ 450j=412\\ \\ j=\frac { 412 }{ 450 }$

So, the answer is: 100

You could multiply both sides of the equation by 100 to get the value of (j) quickly.

6 0

3 years ago

Read 2 more answers