Question

which of the following is an arithmetic sequence? * –20, –25, –30, –35, –45, ... *–15.6, –12.9, –10.2, –7.5, –4.8, ... * 3.1, 6.2, 12.4, 24.8, 49.6, ... * 7.2, 3.6, 1.8, 0.9, 0.45, ...

Answer 1

Answer:

–20, –25, –30, –35, –45 is an arithmetic sequence.

Step-by-step explanation:

An arithmetic sequence is defined by

$T_n=T_1+k(n-1)$

where

$T_n$ is the nth term of the sequence

$T_1$ is the first term of the sequence

$k$ is the difference between consecutive terms.

To find which sequence is arithmetic, let us look at each of the options one by one.

Option 1: –20, –25, –30, –35, –45

It is clear that each next term in this sequence is 5 less than the previous; therefore, this is an arithmetic sequence, and $k=-5$,the formula is

$T_n=-20+-5(n-1)$

Option 2: -15.6,-15.9,-10.2,-7.5,-4.8...

In this sequence there is not any common difference between the terms, for example: -15.6--15.9=0.3,   -15.9--10.2=-5.7   -10.2--7.5=-2.7. Therefore, this not an arithmetic sequence.

Option 3: 3.1, 6.2, 12.4, 24.8, 49.9...

In this sequence there is not any common difference between the terms, for example: 6.2-3.1 =3.1,   12.4-6.2 =6.2, 24.8-12.4 =12.4. So, this is not an arithmetic sequence.

Option 4: 7.2, 3.6, 1.8, 0.9, 0.45....

This sequence also does not have any common difference between the consecutive terms, for example: 7.2-3.6=3.6, 3.6-1.8=1.8, 1.8-0.9=0.9. So this is also not an arithmetic sequence.

Thus only option 1 is the arithmetic sequence.