Question

Consider the arithmetic sequence 10,12,14,16 if n is an integer, which of these functions generate the sequence?

Answer 1

Given:

The arithmetic sequence is:

10, 12, 14, 16, ...

To find:

The function that generates the given sequence if n is an integer.

Solution:

We have,

10, 12, 14, 16, ...

Here, the first term is 10 and the common difference is:

$d=a_2-a_1$

$d=12-10$

$d=2$

The nth term of an arithmetic sequence is:

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

Where, a is the first term, d is the common difference and $n\geq 1$.

Putting $a=10,d=2$ in the above formula, we get

$a_n=10+(n-1)2$

$a_n=10+2n-2$

$a_n=8+2n$

Therefore, the function $a_n=8+2n, n\geq 1$ generates the sequence.