What kind of sequence is this? 1, 10, 100, 1,000, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Observation of Sequence: The given sequence is 1, 10, 100, 1,000, ... We can observe that each term is obtained by multiplying the previous term by 10.Confirmation of Arithmetic Sequence: To confirm if the sequence is arithmetic, we check if the difference between consecutive terms is constant. The difference between the second term (10) and the first term (1) is 10 - 1 = 9. The difference between the third term (100) and the second term (10) is 100 - 10 = 90. Since the differences are not constant, the sequence is not arithmetic.Confirmation of Geometric Sequence: To confirm if the sequence is geometric, we check if the ratio between consecutive terms is constant. The ratio of the second term (10) to the first term (1) is 10 / 1 = 10. The ratio of the third term (100) to the second term (10) is 100 / 10 = 10. Since the ratios are constant, the sequence is geometric.Conclusion: Based on the constant ratio between consecutive terms, we can conclude that the sequence is a geometric sequence.

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What kind of sequence is this? $\newline$ $1, 10, 100, 1,000, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Math Problems

Grade 8

Identify arithmetic and geometric sequences

Full solution

Q. What kind of sequence is this?

\newline

1, 10, 100, 1,000, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Observation of Sequence: The given sequence is $1, 10, 100, 1,000, \ldots$ $\newline$ We can observe that each term is obtained by multiplying the previous term by $10$ .
Confirmation of Arithmetic Sequence: To confirm if the sequence is arithmetic, we check if the difference between consecutive terms is constant. $\newline$ The difference between the second term ( $10$ ) and the first term ( $1$ ) is $10 - 1 = 9$ . $\newline$ The difference between the third term ( $100$ ) and the second term ( $10$ ) is $100 - 10 = 90$ . $\newline$ Since the differences are not constant, the sequence is not arithmetic.
Confirmation of Geometric Sequence: To confirm if the sequence is geometric, we check if the ratio between consecutive terms is constant. $\newline$ The ratio of the second term ( $10$ ) to the first term ( $1$ ) is $\frac{10}{1} = 10$ . $\newline$ The ratio of the third term ( $100$ ) to the second term ( $10$ ) is $\frac{100}{10} = 10$ . $\newline$ Since the ratios are constant, the sequence is geometric.
Conclusion: Based on the constant ratio between consecutive terms, we can conclude that the sequence is a geometric sequence.