Question

Which is the function describe the arithmetic sequence shown ? 3,7,11,15,19,23

Answer 1

$a_n = 4n-1$ is the function describe the arithmetic sequence

Solution:

Given arithmetic sequence is:

3, 7, 11, 15, 19, 23

The nth term of arithmetic sequence is given as:

$a_n = a_1+(n-1)d$

Where,

n is the nth term

d is the common difference between terms

$a_1$ is the first term of sequence

From given,

3, 7, 11, 15, 19, 23

Common difference, d = 7 - 3 = 4

$a_1=3$

Substituting the values in formula,

$a_n = 3 + (n-1) \times 4\\\\a_n = 3 + 4n - 4\\\\a_n = 4n-1$

Where, n is positive integer, $n\geq 1$

Thus the function that describes the arithmetic sequence is found