Question

select the correct answer.

three arithmetic sequences are given below.

sequence a: (5, 7, 9, 11, \dots)
sequence b: (34, 43, 52, 61, \dots)
sequence c: (-9, -4, 1, 6, \dots)

which of the following lists the sequences in order from least common difference to greatest?

b, c, a
a, b, c
c, a, b
a, c, b

Explanation:

⚡ Using what you learned: Arithmetic Sequences

Step 1: Find the common difference of Sequence A

$$ d_A = 7 - 5 = 2 $$

Step 2: Find the common difference of Sequence B

$$ d_B = 43 - 34 = 9 $$

Step 3: Find the common difference of Sequence C

$$ d_C = -4 - (-9) = 5 $$

Step 4: Order from least to greatest common difference

$$ 2 < 5 < 9 \implies A < C < B $$

Answer:

A, C, B