Math Problem Statement

What type of arithmetic sequence is -17, -13, -9, -5

Solution

The given sequence is 17,13,9,5-17, -13, -9, -5.

To determine the type of arithmetic sequence, we first need to find the common difference dd between consecutive terms.

Calculating the common difference: d=13(17)=13+17=4d = -13 - (-17) = -13 + 17 = 4 d=9(13)=9+13=4d = -9 - (-13) = -9 + 13 = 4 d=5(9)=5+9=4d = -5 - (-9) = -5 + 9 = 4

The common difference dd is 44, which is positive.

An arithmetic sequence with a positive common difference is called an increasing arithmetic sequence.

To summarize, the given sequence 17,13,9,5-17, -13, -9, -5 is an increasing arithmetic sequence with a common difference of 44.

If you have any further questions or need more details, please let me know! Here are 8 related questions to expand your understanding:

  1. What is the 10th term of this sequence?
  2. How do you find the sum of the first nn terms in an arithmetic sequence?
  3. What is the general formula for the nn-th term of this sequence?
  4. How do arithmetic sequences differ from geometric sequences?
  5. What is the 20th term of this sequence?
  6. How do you determine if a sequence is arithmetic?
  7. What is the sum of the first 5 terms of this sequence?
  8. How can we graph an arithmetic sequence?

Tip: Understanding the common difference in an arithmetic sequence helps in predicting the behavior of the sequence and determining any term within it using the general formula.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences

Formulas

General formula for the nth term of an arithmetic sequence

Theorems

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Suitable Grade Level

Grades 7-9