Concept explainers
To explain: The common difference of a decreasing arithmetic sequence.
Answer to Problem 4CFU
The common difference of a decreasing arithmetic sequence is negative.
Explanation of Solution
Given information:
The decreasing arithmetic sequence.
Consider the decreasing arithmetic sequence.
Since, the sequence is decreasing this means the terms of the sequence are getting smaller.
Which is only possible when something is subtracted from a preceding term to obtain the next term.
For example: An arithmetic sequence is
Recall that a sequence with first term as
Compute the difference between the consecutive terms,
And
Therefore, common difference is
Common difference is negative.
Thus, the common difference of a decreasing arithmetic sequence is negative.
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