Question

question 20
is the sequence $a_n = 2 + 4n$ arithmetic?
your answer is (input yes or no)
if your answer is yes,
its first term is
its common difference is
question help: video

Explanation:

Step1: Recall arithmetic sequence rule

An arithmetic sequence has the form $a_n = a_1 + (n-1)d$, which can be rewritten as $a_n = (a_1 - d) + dn$, where $a_1$ is the first term and $d$ is the common difference.

Step2: Match given sequence to form

Given $a_n = 2 + 4n$. Compare to $a_n = (a_1 - d) + dn$:

• The coefficient of $n$ is the common difference: $d=4$

Step3: Find first term $a_1$

Substitute $n=1$ into $a_n = 2 + 4n$:
$a_1 = 2 + 4(1) = 6$

Step4: Verify arithmetic sequence

Check the difference between consecutive terms:
$a_{n+1}-a_n = [2+4(n+1)] - [2+4n] = 2+4n+4-2-4n = 4$, a constant. So it is arithmetic.

Answer:

yes
6
4