Question

1. determine whether the sequences below are arithmetic, geometric, or neither.

a) 2, 5, 10, 17, ....
b) 18, 15, 12, 9, ....
c) -3, 6, -12, 24, ....

Explanation:

Step1: Check sequence a) for arithmetic

Calculate consecutive differences:
$5-2=3$, $10-5=5$, $17-10=7$

Step2: Check sequence a) for geometric

Calculate consecutive ratios:
$\frac{5}{2}=2.5$, $\frac{10}{5}=2$, $\frac{17}{10}=1.7$

Step3: Classify sequence a)

Differences/ratios not constant → neither

Step4: Check sequence b) for arithmetic

Calculate consecutive differences:
$15-18=-3$, $12-15=-3$, $9-12=-3$

Step5: Classify sequence b)

Differences are constant → arithmetic

Step6: Check sequence c) for geometric

Calculate consecutive ratios:
$\frac{6}{-3}=-2$, $\frac{-12}{6}=-2$, $\frac{24}{-12}=-2$

Step7: Classify sequence c)

Ratios are constant → geometric

Answer:

a) Neither
b) Arithmetic
c) Geometric