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Recognizing Arithmetic Sequences

Recognizing Arithmetic Sequences 1.14 - Solution

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We have been given the following arithmetic sequence, and we need to decide whether 66 or -6\text{-}6 is the common difference. 25,19,13,7 25,19,13,7\ldots Let's look for a relation between the terms. 25619613676 25\xrightarrow{{\color{#0000FF}{-6}}}19\xrightarrow{{\color{#0000FF}{-6}}}13\xrightarrow{{\color{#0000FF}{-6}}}7\xrightarrow{{\color{#0000FF}{-6}}}\ldots As we can see, each new term is found by subtracting 66 from the previous term. Therefore, the common difference is -6.\text{-}6.