Question

Which function below represents the arithmetic sequence 3, 7, 11, 15...? . f(n) = 4 + 3(n – 1). f(n) = 4 + 3n. f(n) = 3 + 4n. f(n) = 3 + 4(n – 1)

Answer 1

The given above is an arithmetic sequence with first term equal to 3 and the common difference equal to 4. That is from 7 - 3 = 11 - 7 = 15 - 11. The nth term of an arithmetic sequence is given by the equation,
                                        an = a1 + (n - 1) x d
Substituting the given,
                                        an = 3 + 4(n - 1)
thus, the answer is the fourth choice. 

Answer 2

Answer: $f(n)=3+4(n-1)$

Step-by-step explanation:

The given arithmetic sequence : 3, 7, 11, 15...

Here , the first term = $a_1=3$

Common difference =$d=a_2-a_1=7-3=4$

We know that function represents any Arithmetic sequence is given by :-

$f(n)=a_1+(n-1)d$ , where n= Number of term= 1,2,3,4....

$a_1$ is the first term.

d= common difference.

For the given sequence , the function would be :-

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

Hence, the function represents the given arithmetic sequence :

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