Which of the sequences is an arithmetic sequence?A.1, 5, 10, 15, 20, ...B.12, –24, 36, –48, 60, ...C.154, 71, 8, 5, 2, ...D.–20, –27, –34, –41, –48, ...SUBMITarrow_backPREVIOUS
Question
Which of the sequences is an arithmetic sequence?A.1, 5, 10, 15, 20, ...B.12, –24, 36, –48, 60, ...C.154, 71, 8, 5, 2, ...D.–20, –27, –34, –41, –48, ...SUBMITarrow_backPREVIOUS
Solution
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is called the common difference.
Let's check each option:
A. 1, 5, 10, 15, 20, ... The difference between consecutive terms is 5-1=4, 10-5=5, 15-10=5, 20-15=5. The difference is not constant, so this is not an arithmetic sequence.
B. 12, –24, 36, –48, 60, ... The difference between consecutive terms is -24-12=-36, 36-(-24)=60, -48-36=-84, 60-(-48)=108. The difference is not constant, so this is not an arithmetic sequence.
C. 154, 71, 8, 5, 2, ... The difference between consecutive terms is 71-154=-83, 8-71=-63, 5-8=-3, 2-5=-3. The difference is not constant, so this is not an arithmetic sequence.
D. –20, –27, –34, –41, –48, ... The difference between consecutive terms is -27-(-20)=-7, -34-(-27)=-7, -41-(-34)=-7, -48-(-41)=-7. The difference is constant, so this is an arithmetic sequence.
So, the answer is D. –20, –27, –34, –41, –48, ...
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