Question

which sequence is not an arithmetic sequence? 12, 18, 24, 30,... 10, 3, -4, -11,... 2, 4, 8, 16,... 16, 20, 24, 28,...

Explanation:

Step1: Define arithmetic sequence

An arithmetic sequence has a constant difference $d = a_{n+1}-a_n$ between consecutive terms.

Step2: Check yellow sequence

Calculate differences:
$18-12=6$, $24-18=6$, $30-24=6$. Constant $d=6$, so it is arithmetic.

Step3: Check purple sequence

Calculate differences:
$3-10=-7$, $-4-3=-7$, $-11-(-4)=-7$. Constant $d=-7$, so it is arithmetic.

Step4: Check orange sequence

Calculate differences:
$4-2=2$, $8-4=4$, $16-8=8$. Differences are not constant, so it is not arithmetic.

Step5: Check green sequence

Calculate differences:
$20-16=4$, $24-20=4$, $28-24=4$. Constant $d=4$, so it is arithmetic.

Answer:

2, 4, 8, 16,...