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.
