Math Problem Statement

Show Examples Find the common difference of the arithmetic sequence .−19,−11,−3,...

Solution

To find the common difference in an arithmetic sequence, we subtract the first term from the second term. Given the sequence:

19,11,3,-19, -11, -3, \dots

we can find the common difference, dd, by subtracting 19-19 from 11-11:

d=11(19)=11+19=8d = -11 - (-19) = -11 + 19 = 8

So, the common difference dd is 8.

Would you like further explanation or have any questions about this process?

Here are 5 related questions to help reinforce the concept:

  1. How would you find the 10th term in this sequence?
  2. How can we determine the formula for the nn-th term of an arithmetic sequence?
  3. What is an example of an arithmetic sequence with a common difference of -5?
  4. How can we tell if a sequence is arithmetic based on its terms?
  5. What happens to the terms of an arithmetic sequence if the common difference is 0?

Tip: In an arithmetic sequence, the difference between consecutive terms is always constant, which is why we call it the "common difference."

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Common Difference
Sequences

Formulas

d = a2 - a1, where d is the common difference and a1, a2 are consecutive terms

Theorems

Definition of an Arithmetic Sequence

Suitable Grade Level

Grades 6-8