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kondaur [170]
3 years ago
8

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively. Pl

ease explain this to me very carefully.
Mathematics
2 answers:
kicyunya [14]3 years ago
8 0
Hello,

u_{0} =a\\
 u_{1} =a*r\\
 u_{2} =a*r^{2}=-6\\
 u_{3} =a*r^{3}\\
 u_{4} =a*r^{4}\\
 u_{5} =a*r^{5}=162\\
....\\
\boxed{ u_{n} =a*r^{n}} \\

\dfrac{ 162}{-6} = \dfrac{ u_{5} }{ u_{3}} = \dfrac{ a*r^{5}}{ a*r^{2}} =r^3= -27\\
==\ \textgreater \  r=-3\\

 u_{2} =a*r^{2}=-6=a*(-3)^2 \ ==\ \textgreater \  a=-\frac{6}{9} =-\frac{2}{3}\\


\boxed{ u_{n} =-\frac{2}{3}*(-3)^{n}=(-1)^{n+1}*2*3^{n-1}} \\


ki77a [65]3 years ago
4 0
The first step is to determine the equations used in the geometric sequences of the second and fifth terms. For the second term, the formula is -6=a*r². The equation for the fifth term is 162=a*r⁵. Therefore, the general formula is uₓ=a*rⁿ.
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77julia77 [94]

Answer:

2 out of 5

Step-by-step explanation:

I believe that 96/240 needs to be simplified until it cant anymore, an that is the probability because they both fit three, I will divide by three.

96/3=32

240/3= 80

<u>32/80</u>

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16/40 then because they both fit four, Ill do four.

4/10then 2 again

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6 0
3 years ago
Can someone please help me
rewona [7]

\quad \huge \quad \quad \boxed{ \tt \:Answer }

\qquad \tt \rightarrow \: f(0) = -3

\qquad \tt \rightarrow \: f(2) = 1

\qquad \tt \rightarrow \: f(4) = 1

____________________________________

\large \tt Solution  \: :

F(x) represents the value of y on curve for given value of x

\textsf{\large First -}

\qquad \tt \rightarrow \: f(0) =( 0) {}^{2}  - 3

[ since 0 < 2 ]

\qquad \tt \rightarrow \: f(0) = 0 {}^{}  - 3

\qquad \tt \rightarrow \: f(0) =   - 3

\textsf{\large Second}

\qquad \tt \rightarrow \: f(2) =   (2) {}^{2}  - 3

[ since 2 = 2 ]

\qquad \tt \rightarrow \: f(2) =   4{}^{}  - 3

\qquad \tt \rightarrow \: f(2) =   1

\textsf{\large Third -}

\qquad \tt \rightarrow \: f(4) =    - 4 + 5

[ since 4 > 2 ]

\qquad \tt \rightarrow \: f(4) =    1

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

4 0
1 year ago
What is the solution set of {x | x &lt; -3} ∩ {x | x &gt; 5}?
solniwko [45]

x <-3 includes the numbers-4, -5, -6..........

x> 5 includes the numbers 6, 7 , 8.....

here we have to find intersection of these two.

By intersection we mean the values of x that occur in both the sets,

here there is no number or value of x that occur in both the sets.

So answer is empty set

5 0
3 years ago
I domt understand slope at all
photoshop1234 [79]

slope = 2 and y-intercept = 0

the equation of a line in ' slope- intercept form ' is

y = mx + c  ( mis the slope and c the y-intercept )

given 2x - y = 0 ( add y to both sides )

2x = y or y = 2x + 0 ← in slope-intercept form

with slope m = 2 and y-intercept c = 0


7 0
2 years ago
I'm stuck on this problem-3+7
Semmy [17]
The answer to -3 + 7 is 4
4 0
3 years ago
Read 2 more answers
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