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Select the correct answer. Which type of sequence is shown? 5, 10, 15, 20, 25,... arithmetic both arithmetic and geometric neither arithmetic nor geometric geometric

Answer :

Solution:

Given the sequence;

[tex]5,10,15,20,25,...[/tex]

An arithmetic sequence is a sequence with a common difference, d. And a geometric sequence is a sequence with a common ratio, r.

[tex]\begin{gathered} d=a_2-a_1=a_3-a_2 \\ \\ d=10-5=15-5 \\ \\ d=5 \end{gathered}[/tex]

While;

[tex]\begin{gathered} r=\frac{a_2}{a_1}=\frac{a_3}{a_2} \\ \\ \frac{10}{5}\ne\frac{15}{10} \end{gathered}[/tex]

Hence, the sequence has only a common difference.

CORRECT OPTION: Arithmetic

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