Question

Which of these are arithmetic sequences?

Answer 1

A sequence of numbers is said to arithmetic if any couple of adjacent terms differ by the same number. That number is said to be the common difference of the sequence. Let's see what the differences are for each sequence:

First sequence

Difference between the first two terms:

$1 - (-3) = 4$

Difference between the third and second terms:

$5 - 1 = 4$

Difference between the fourth and third terms:

$9-5 = 4$

The difference is constant, so this sequence is an arithmetic sequence.

Second sequence

Difference between the first two terms:

$2 - 1 = 1$

Difference between the third and second terms:

$4-2 = 2$

The difference is not constant, so this sequence is not an arithmetic sequence.

Third sequence

Difference between the first two terms:

$-12 - 4 = -16$

Difference between the third and second terms:

$36 - (-12) = 36+12 = 48$

The difference is not constant, so this sequence is not an arithmetic sequence.

Fourth sequence

Difference between the first two terms:

$14 - 7 = 7$

Difference between the third and second terms:

$21 - 14 = 7$

Difference between the fourth and third terms:

$28 - 21 = 7$

The difference is constant, so this sequence is an arithmetic sequence.