Question

What is the nth term rule of the linear sequence below?

Answer 1

Answer:

$a_n=5+2n$

Step-by-step explanation:

Each term is 2 more than the previous term, so the common difference is 2.

Let $a_n$ be the nth term of the sequence. Then, the first term is $a_1=7$.

The second term is $a_2=7+2=9$, and the third term is $a_3=7+2+2=11$.

Therefore, every term can be written as

$a_n=7+\underbrace{2+2\cdots +2}_{n-1~\text{times}}$.

Since repeated addition is multiplication, this can be written as

$a_n=7+2(n-1),$

which is the nth term rule of the linear sequence.

This could also be expanded to $\boxed{a_n=5+2n.}$