Which best describes the relationship between the successive terms in the sequence shown?

9, -1, -11, -21, ...

A. The common difference is -10.
B. The common difference is 10.
C. The common ratio is -9.
D. The common ratio is 9.

Calculate the difference between consecutive terms: − 1 − 9 = − 10 , − 11 − ( − 1 ) = − 10 , − 21 − ( − 11 ) = − 10 .
Calculate the ratio between consecutive terms: 9 − 1 ​ , − 1 − 11 ​ , − 11 − 21 ​ .
Since the difference is constant (-10), the sequence has a common difference.
The common difference is -10, so the answer is: The common difference is -10. ​

Explanation

Analyzing the Sequence We are given the sequence 9, -1, -11, -21, ... and asked to determine the relationship between successive terms. We need to check if there is a common difference or a common ratio.

Calculating the Common Difference To check for a common difference, we subtract each term from the subsequent term: − 1 − 9 = − 10 − 11 − ( − 1 ) = − 11 + 1 = − 10 − 21 − ( − 11 ) = − 21 + 11 = − 10 Since the difference between consecutive terms is constant, the sequence has a common difference.

Checking for a Common Ratio To check for a common ratio, we divide each term by the preceding term: 9 − 1 ​ = − 9 1 ​ − 1 − 11 ​ = 11 − 11 − 21 ​ = 11 21 ​ Since the ratio between consecutive terms is not constant, the sequence does not have a common ratio.

Conclusion The common difference is -10. Therefore, the correct answer is 'The common difference is -10'.


Examples
Sequences with a common difference (arithmetic sequences) appear in various real-life scenarios, such as calculating simple interest, where the interest earned each year is constant. For example, if you deposit $100 into an account that earns $5 every year, the sequence of your account balance would be an arithmetic sequence: $100, $105, $110, $115, and so on. Understanding arithmetic sequences helps in predicting future values in such scenarios.

Answered by GinnyAnswer | 2025-07-03

The relationship between the successive terms in the sequence 9, -1, -11, -21 is characterized by a common difference of -10. Therefore, the answer is 'The common difference is -10.'
;

Answered by Anonymous | 2025-07-04