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expeople1 [14]
2 years ago
5

Can somebody help me out?

Mathematics
1 answer:
Viefleur [7K]2 years ago
5 0

Answer:

Yeah

Step-by-step explanation:

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Find the general term of sequence defined by these conditions.
disa [49]

Answer:

\displaystyle  a_{n}  =     (2)^{2n -1}   -   (3) ^{n-1 }

Step-by-step explanation:

we want to figure out the general term of the following recurrence relation

\displaystyle \rm a_{n + 2} - 7a_{n + 1} + 12a_n = 0  \:  \: where :  \:  \:a_1 = 1 \: ,a_2 = 5,

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e

  • {x}^{n}  =  c_{1} {x}^{n - 1}  + c_{2} {x}^{n - 2}  + c_{3} {x}^{n -3 } { \dots} + c_{k} {x}^{n - k}

the steps for solving a linear homogeneous recurrence relation are as follows:

  1. Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
  2. Solve the polynomial by factoring or the quadratic formula.
  3. Determine the form for each solution: distinct roots, repeated roots, or complex roots.
  4. Use initial conditions to find coefficients using systems of equations or matrices.

Step-1:Create the characteristic equation

{x}^{2}  - 7x+ 12= 0

Step-2:Solve the polynomial by factoring

factor the quadratic:

( {x}^{}  - 4)(x - 3) =  0

solve for x:

x =  \rm 4 \:and \: 3

Step-3:Determine the form for each solution

since we've two distinct roots,we'd utilize the following formula:

\displaystyle a_{n}  = c_{1}  {x} _{1} ^{n }  + c_{2}  {x} _{2} ^{n }

so substitute the roots we got:

\displaystyle a_{n}  = c_{1}  (4)^{n }  + c_{2}  (3) ^{n }

Step-4:Use initial conditions to find coefficients using systems of equations

create the system of equation:

\begin{cases}\displaystyle 4c_{1}    +3 c_{2}    = 1  \\ 16c_{1}    + 9c_{2}     =  5\end{cases}

solve the system of equation which yields:

\displaystyle c_{1}  =  \frac{1}{2}     \\  c_{2}   =   - \frac{1}{3}

finally substitute:

\displaystyle  a_{n}  =  \frac{1}{2}   (4)^{n }   -  \frac{1}{3}  (3) ^{n }

\displaystyle \boxed{ a_{n}  =    (2)^{2n-1 }   -   (3) ^{n -1}}

and we're done!

7 0
3 years ago
What is the answer to this math problem......
Anna [14]
The answer is 20 pounds.
5 0
3 years ago
Read 2 more answers
What is g(x) I need your help
velikii [3]

Answer:

D ,  i thinks this is the answer  because i cant see the g(x) good

Step-by-step explanation:

5 0
3 years ago
Will give brainliest for *BEST* answer!
Nataliya [291]
Use substitution and substitute y into the other equation. One of the equations already gives you y in terms of x, so use that and substitute it into the other equation. y = 3x - 4

Plug into the other equation: -3y = -9x + 12 
-3(3x-4) = -9x + 12
-9x + 12 = -9x + 12
This is an identity. So that means that any value of x makes this equation true. So B.
8 0
3 years ago
Special right triangles find the missing side lengths. Leave your answers as radicals in simplest form. Need help ASAP due tomor
Soloha48 [4]

Answer:

Step-by-step explanation:

5 0
3 years ago
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