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2022-10-10

Determine whether the sequence 5,15,45,135,... is geometric and if it is, what is the common ratio

Jase Powell

Beginner2022-10-11Added 11 answers

Sequence : 5,15,45,135,.......

${a}_{1}=5,{a}_{2}=15,{a}_{3}=45,{a}_{4}=135,.......$

$\frac{{a}_{2}}{{a}_{1}}=\frac{15}{5}=3,\frac{{a}_{3}}{{a}_{2}}=\frac{45}{15}=3,\frac{{a}_{4}}{{a}_{3}}=\frac{135}{45}=3,.....$

In this sequence the ratio of each term and the previous term is

constant , so it is geometric sequnce and constant is 3.

Common ratio is 3

${a}_{1}=5,{a}_{2}=15,{a}_{3}=45,{a}_{4}=135,.......$

$\frac{{a}_{2}}{{a}_{1}}=\frac{15}{5}=3,\frac{{a}_{3}}{{a}_{2}}=\frac{45}{15}=3,\frac{{a}_{4}}{{a}_{3}}=\frac{135}{45}=3,.....$

In this sequence the ratio of each term and the previous term is

constant , so it is geometric sequnce and constant is 3.

Common ratio is 3

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