Question

is each sequence arithmetic? how do you know?

1. 7, 9, 12, 16, ...
2. 35, 43, 51, 59, ...

Explanation:

Step1: Check sequence 13 for constant difference

Calculate consecutive differences:
$9 - 7 = 2$
$12 - 9 = 3$
$16 - 12 = 4$

Step2: Evaluate sequence 13's differences

Differences (2, 3, 4) are not equal.

Step3: Check sequence 14 for constant difference

Calculate consecutive differences:
$43 - 35 = 8$
$51 - 43 = 8$
$59 - 51 = 8$

Step4: Evaluate sequence 14's differences

All differences equal 8, a constant.

Answer:

1. No, the differences between consecutive terms are not constant (2, 3, 4, ...).
2. Yes, the difference between each pair of consecutive terms is a constant 8.