What is the nth term rule of the quadratic sequence

Ответ:

katelynamber10

01.06.2020

Let the nth term be given by the expression an²+bn+c.

We can write A: -7=a+b+c B: -6=4a+2b+c C: -3=9a+3b+c

D: B-A: 1=3a+b
E: C-B: 3=5a+b
E-Dm 2=2a, a=1, b=1-3=-2, c=-7-1+2=-6.

So the expression for the nth term is n²-2n-6.

Put n=4: 16-8-6=2 which fits the sequence.
Put n=5: 25-10-6=9 which also fits the sequence.
So the nth term is

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Ответ:

pitmmaKaos5499

07.09.2020

Mathematics

$\large\begin{array}{l} \textsf{Solve the absolute value inequality:}\\\\ \mathsf{|x-7|+5\ge 3}\\\\ \mathsf{|x-7|\ge 3-5}\\\\ \mathsf{|x-7|\ge -2}\\\\\\ \textsf{Since absolute values always give a non-negative number,}\\\textsf{every real value for x satisfies the inequatily:}\\\\ \textsf{For all }\mathsf{x\in\mathbb{R},}\\\\ \mathsf{|x-7|\ge 0-2}\\\\\\ \therefore~~\mathsf{|x-7|\ge 2}\\\\ \textsf{regardless of the value of x.} \end{array}$

$\large\begin{array}{l} \textsf{Solution set: }\mathsf{S=\mathbb{R}.} \end{array}$

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$\large\textsf{I hope this helps. :-)}$

Tags: absolute value inequatily solve solution algebra

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What is the nth term rule of the quadratic sequence below? − 7 , − 6 , − 3 , 2 , 9 , 18 , 29 , .

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