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Oliga [24]
2 years ago
13

What is the nth term of the sequence -2 -8 -18 -32 -50

Mathematics
1 answer:
andreev551 [17]2 years ago
6 0

Answer:

-2n²

Step-by-step explanation:

Using the image attached:
We see that the second differences (blue ones) are all equal so we conclude that this is a quadratic sequence.
The quadratic sequence has the form:
T_{n} = an^{2}  +bn +c

To find the value of a we just divide second difference ( -4 ) by 2:

  • a = \frac{-4}{2}= -2

Now we have:

  • T_{n}= -2n^{2}  +bn+c

Substitute n_{1} and n_{2} into the equation above:

  • T_{1} = -2(1)^{2}  +b(1) +c
  • T_{2} = -2(2)^{2}  +b(2)+c

Since T_{1} = -2 and T_{2} = -8 , after simplification we have:

  • b +c =0
  • 2b+c=0

The solution of this system is:

  • b=0, c =0

The general term is :

T_{n} = -2n^{2}

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Use the theorem in Sec. 28 to show that if f (z) is analytic and not constant throughout a domain D, then it cannot be constant
alexandr1967 [171]

Answer:

The value of f(z) is not constant in any neighbourhood of D. The proof is as explained in the explaination.

Step-by-step explanation:

Given

For any given function f(z), it is analytic and not constant throughout a domain D

To Prove

The function f(z) is non-constant constant in the neighbourhood lying in D.

Proof

1-Assume that the value of f(z)  is analytic and has a constant throughout some neighbourhood in D which is ω₀

2-Now consider another function F₁(z) where

F₁(z)=f(z)-ω₀

3-As f(z) is analytic throughout D and F₁(z) is a difference of an analytic function and a constant so it is also an analytic function.

4-Assume that the value of F₁(z) is 0 throughout the domain D thus F₁(z)≡0 in domain D.

5-Replacing value of F₁(z) in the above gives:

F₁(z)≡0 in domain D

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f(z)≡0+ω₀ in domain D

f(z)≡ω₀ in domain D

So this indicates that the value of f(z) for all values in domain D is a constant  ω₀.

This contradicts with the initial given statement, where the value of f(z) is not constant thus the assumption is wrong and the value of f(z) is not constant in any neighbourhood of D.

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To learn more about depreciation, please check: brainly.com/question/25552427

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2 years ago
What is the sum of the difference?
Alona [7]

Answer:

A. 9x^4 and 3x^5y

Step-by-step explanation:

there are two ways to solve this:

first way:

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the second way is the regular way

when you add or subtract numbers with variables and exponents you want to add the constants and add the exponents in this case 5x^{4} +4x^2 is the same as (5x+4x)^(4+4) = 9x^4and you can do the same process for subtraction

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