Question

Given the sequence 3, 7, 11, 15, ........ where x = 1, 2......, what is the function rule? f(x) = 4
f(x)=4x+3
f(x)=3
f(x) = 4x − 1

Answer 1

Answer:

f(x)=4x-1

Step-by-step explanation:

The given sequence is 3, 7, 11, 15, ........ where x = 1, 2.....

We want to write a function rule for this sequence.

The first term of this sequence is $f(1)=3$

The common difference of this sequence is d=7-3=4

The function rule is given by:

$f(x)=f(1)+d(x-1)$

We substitute these values to get:

$f(x)=3+4(x-1)$

We simplify to get:

$f(x)=3+4x-4$

$f(x)=4x-1$

Answer 2

Answer:

$f(x)=4x-1$ is the function rule.

Step-by-step explanation:

Given the sequence

$3, 7, 11, 15, ........$

As the common difference is

$d\:=\:7-3\:=\:4$, $d\:=\:11\:-\:7\:=\:4$

So, this sequence is in Arithmetic progression

As

$f\left(1\right)=a_1=3$  and $d=4$

So,

The function rule will be:

$f(x)=f(1)+d(x-1)$

$f(x)=3+4(x-1)$

$f(x)=3+4x-4$

$f(x)=4x-1$

Keywords: function, sequence, arithmetic

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