Question

10
determine whether each sequence is an arithmetic sequence.

	arithmetic sequence	not an arithmetic sequence
1.5, 4.5, 7.5, 10.5, ...
8, 10, 12, 14, ...
9, 5, 1, -3, ...
-2, 8, -18, 28, ...

Explanation:

Step1: Define arithmetic sequence

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

Step2: Test sequence 3, 6, 12, 24, ...

Calculate differences:
$6-3=3$, $12-6=6$, $24-12=12$.
Differences are not constant.

Step3: Test sequence 1.5, 4.5, 7.5, 10.5, ...

Calculate differences:
$4.5-1.5=3$, $7.5-4.5=3$, $10.5-7.5=3$.
Differences are constant ($d=3$).

Step4: Test sequence 8, 10, 12, 14, ...

Calculate differences:
$10-8=2$, $12-10=2$, $14-12=2$.
Differences are constant ($d=2$).

Step5: Test sequence 9, 5, 1, -3, ...

Calculate differences:
$5-9=-4$, $1-5=-4$, $-3-1=-4$.
Differences are constant ($d=-4$).

Step6: Test sequence -2, 8, -18, 28, ...

Calculate differences:
$8-(-2)=10$, $-18-8=-26$, $28-(-18)=46$.
Differences are not constant.

Answer:

Sequence	Arithmetic Sequence	Not an Arithmetic Sequence
1.5, 4.5, 7.5, 10.5, ...	✓
8, 10, 12, 14, ...	✓
9, 5, 1, -3, ...	✓
-2, 8, -18, 28, ...		✓