Formula for 4,9,14 19

Mathematics

2 answers:

alexira [117]2 years ago

4 0

Answer:

$a_{n }$ = 5n - 1

Step-by-step explanation:

There is a common difference between consecutive terms , that is

9 - 4 = 14 - 9 = 19 - 14 = 5

This indicates the sequence is arithmetic with nth term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 4 and d = 5 , then

$a_{n}$ = 4 + 5(n - 1) = 4 + 5n - 5 = 5n - 1

Alex777 [14]2 years ago

3 0

Answer:

nth term = 5n - 1.

Step-by-step explanation:

This is an arithmetic sequence.

First term a = 4 and common difference d = 5.

nth term = a + d(n -1)

= 4 + 5(n - 1)

= 5n + 4 - 5

= 5n - 1

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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 $x=4$