Addison is writing a poem. She writes 5 words on the first line, 10 words on the second line, 20 words on the third line, and 40 words on the fourth line. What kind of sequence is this? Choices: (A)arithmetic (B)geometric (C)both (D)neither

Question

Addison is writing a poem. She writes 5 words on the first line, 10 words on the second line, 20 words on the third line, and 40 words on the fourth line. What kind of sequence is this?     Choices: (A)arithmetic (B)geometric (C)both (D)neither

Bytelearn · Accepted Answer

Identify Sequence Type: To determine the type of sequence, we need to look at the pattern of the word count in each line. The word counts are 5, 10, 20, and 40 for the first, second, third, and fourth lines, respectively.Check for Arithmetic Sequence: We will first check if the sequence is arithmetic by finding the difference between consecutive terms. The difference between the second and the first term is 10 - 5 = 5. The difference between the third and the second term is 20 - 10 = 10. Since these differences are not the same, the sequence is not arithmetic.Check for Geometric Sequence: Next, we will check if the sequence is geometric by finding the ratio between consecutive terms. The ratio of the second to the first term is 10 / 5 = 2. The ratio of the third to the second term is 20 / 10 = 2. The ratio of the fourth to the third term is 40 / 20 = 2. Since these ratios are the same, the sequence is geometric.

Full solution

More problems from Identify arithmetic and geometric sequences

Related topics

Addison is writing a poem. She writes 555 words on the first line, 101010 words on the second line, 202020 words on the third line, and 404040 words on the fourth line. What kind of sequence is this?\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither