Math Problem Statement

50, 25, 0, -25, -50

Solution

The sequence provided: 50, 25, 0, -25, -50 appears to be an arithmetic sequence. Let's break it down:

  • The first term (a₁) is 50.
  • The second term (a₂) is 25.
  • The third term (a₃) is 0.
  • The fourth term (a₄) is -25.
  • The fifth term (a₅) is -50.

To confirm it's an arithmetic sequence, we check if the difference between consecutive terms is constant.

  • a2a1=2550=25a_2 - a_1 = 25 - 50 = -25
  • a3a2=025=25a_3 - a_2 = 0 - 25 = -25
  • a4a3=250=25a_4 - a_3 = -25 - 0 = -25
  • a5a4=50(25)=25a_5 - a_4 = -50 - (-25) = -25

Since the common difference (d) is -25, this is indeed an arithmetic sequence with a common difference of -25.

The general formula for the nn-th term of an arithmetic sequence is:

an=a1+(n1)da_n = a_1 + (n-1) \cdot d

Here:

  • a1=50a_1 = 50
  • d=25d = -25

Thus, the general term for the sequence is:

an=50+(n1)(25)a_n = 50 + (n-1)(-25)

Would you like to explore any specific details about this sequence?

Here are some related questions to consider:

  1. What would be the 10th term in this arithmetic sequence?
  2. How can you find the sum of the first 20 terms of the sequence?
  3. Can you find the formula for the sum of this arithmetic sequence?
  4. What are some real-world examples of arithmetic sequences like this one?
  5. How does this sequence compare to a geometric sequence?

Tip: The common difference in arithmetic sequences can also help you easily find any term, without listing all the preceding ones!

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Algebra

Formulas

General formula for an arithmetic sequence: a_n = a_1 + (n-1) * d

Theorems

Arithmetic Sequence Common Difference Theorem

Suitable Grade Level

Grades 7-9