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

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

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)`

Answer 2

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.