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Sagot :
The general formula of an arithmetic sequence is:
[tex]a_n=a_1+(n-1)\cdot d[/tex]Where d is known as the common difference and it represents the distance between consecutive terms of the sequence. So we can calculate this distance for each of the four options:
[tex]\begin{gathered} 768,192,48,12,3 \\ 768-192=576 \\ 192-48=144 \end{gathered}[/tex]So in the first sequence the difference between terms is not even constant so this is not the correct option.
[tex]\begin{gathered} 31-35=-4 \\ 27-31=-4 \\ 23-27=-4 \\ 19-23=-4 \end{gathered}[/tex]In the second sequence the distance is -4 so this is a possible answer.
[tex]\begin{gathered} 20-24=-4 \\ 16-20=-4 \\ 4-16=-12 \\ 0-4=-4 \end{gathered}[/tex]In the third sequence the distance is not always the same so we can discard this option.
[tex]\begin{gathered} -20-5=-25 \\ 80-(-20)=100 \end{gathered}[/tex]Here the distance isn't constant so the fourth option can also be discarded.
Then the only sequence with a distance d=-4 is the second option.
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