Determine whether the sequence $\ln 7 , \ln 14 , \ln 21 , \ln 28 , \ldots$ is arithmetic. If so, find the common difference.
A)arithmetic; 14
B)arithmetic; 2
C)arithmetic;7
D)arithmetic; 28
E)not arithmetic

Question

Quizplus · Accepted Answer

The sequence is not arithmetic because the difference between consecutive terms is not constant. In an arithmetic sequence, the difference between any two successive terms is the same. Here, the sequence is given by the natural logarithm of consecutive multiples of 7 ($\ln 7, \ln 14, \ln 21, \ln 28, \ldots$). The difference between successive terms, for example, $\ln 14 - \ln 7 = \ln(14/7) = \ln 2$ and $\ln 21 - \ln 14 = \ln(21/14) = \ln(3/2)$, is not constant. Therefore, the sequence is not arithmetic.

Determine Whether the Sequence ln⁡7,ln⁡14,ln⁡21,ln⁡28,…\ln 7 , \ln 14 , \ln 21 , \ln 28 , \ldotsln7,ln14,ln21,ln28,…

Determine Whether the Sequence $\ln 7 , \ln 14 , \ln 21 , \ln 28 , \ldots$