Math Problem Statement

Find the common difference of the arithmetic sequence minus, 19, comma, minus, 14, comma, minus, 9, comma, point, point, .−19,−14,−9,...

Solution

To find the common difference dd of an arithmetic sequence, we subtract the first term from the second term or any successive term from its previous one.

The given arithmetic sequence is: 19,14,9,-19, -14, -9, \dots

Let's subtract the first term from the second term: d=14(19)=14+19=5d = -14 - (-19) = -14 + 19 = 5

Thus, the common difference dd is 55.

Would you like a deeper explanation or any additional details?

Here are 5 questions related to arithmetic sequences to explore further:

  1. How do you find the nn-th term of an arithmetic sequence?
  2. Can you calculate the sum of the first nn terms of this sequence?
  3. How would the sequence change if the common difference were negative?
  4. What happens if the first term of the sequence changes?
  5. How can arithmetic sequences model real-world situations?

Tip: In an arithmetic sequence, the common difference is always constant between consecutive terms!

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Common Difference

Formulas

d = a_n - a_(n-1)

Theorems

Arithmetic Sequence Property: The difference between consecutive terms is constant.

Suitable Grade Level

Grades 6-8