Question

Which table represents an arithmethic sequence?

Answer 1

Table 3  represents an arithmetic sequence.

Solution:

To find which table represents an arithmetic sequence:

In arithmetic sequence difference of each term is equal.

$d=a_n-a_{n-1}$

Table 1:

$d=a_2-a_1$

  = –12 – (–6)

d = –6

$d=a_3-a_2$

  = –24 – (–12)

d = –12

Here differences are not equal.

So table 1 not represents an arithmetic sequence.

Table 2:

$d=a_2-a_1$

  = 9 – 7

d = 2

$d=a_3-a_2$

  = 13 – 9

d = 4

Here differences are not equal.

So table 2 not represents an arithmetic sequence.

Table 3:

$d=a_2-a_1$

  = 7.3 – 8.7

d = –1.4

$d=a_3-a_2$

  = 5.9 – 7.3

d = –1.4

$d=a_4-a_3$

  = 4.5 – 5.9

d = –1.4

$d=a_5-a_4$

  = 3.1 – 4.5

d = –1.4

Here differences are equal.

So table 3 represents an arithmetic sequence.