What is the sum of the arithmetic sequence 149, 135, 121, …, if there are 28 terms?

1 answer:

andrey2020 [161]3 years ago

3 0

I needed my brother to help me with this one,so here is the answer.
The common difference is -14.

Let's simplify this by expressing each term as 
163 - 14n 
where n is the number of the term. 

Then the sum of the 28 terms is 
28 * 163 - 14 (1+2+3+...+28) 
= 4,564 - 14 * 28 * 29 / 2 
= -1,120

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Given a polynomial f(x), if (x − 4) is a factor, what else must be true?

ollegr [7]

Answer:

$f(4)=0$

Step-by-step explanation:

The Remainder Theorem states that when you divide a polynomial $f(x)$ by a linear factor $(x-a)$ , where $a$ is a constant, the remainder is $f(x)$ evaluated at $x=a$

Moreover, according to the Factor Theorem, an extension of the Remainder Theorem, if the remainder of the function $f(x)$ is 0 when evaluated at $x=a$ , then $(x-a)$ is said to be a factor of the polynomial $f(x)$

Given the 2 theorems above, it follows that if $(x-4)$ is a factor of $f(x)$ , then the remainder is equal to 0 when $f(x)$ is evaluated at $x=4$