Math Problem Statement

Find the ​twenty-eighth term of the arithmetic sequence 22​, 21​, 20​, ... Question content area bottom Part 1 a 28 equals    enter your response here ​(Simplify your​ answer.)

Solution

To find the 28th term (a28a_{28}) of the given arithmetic sequence, we use the formula for the nn-th term of an arithmetic sequence:

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

Given:

  • a1=22a_1 = 22 (the first term),
  • d=1d = -1 (common difference, calculated as 2122=121 - 22 = -1),
  • n=28n = 28 (term number to find).

Substituting into the formula:

a28=22+(281)(1)a_{28} = 22 + (28-1)(-1) a28=22+27(1)a_{28} = 22 + 27(-1) a28=2227a_{28} = 22 - 27 a28=5a_{28} = -5

Final Answer:

a28=5a_{28} = -5

Would you like a detailed explanation or further clarification? Here are 5 related questions you might find interesting:

  1. What is the sum of the first 28 terms of this sequence?
  2. How do we determine the common difference in an arithmetic sequence?
  3. Can we derive the general formula for any term in this sequence?
  4. What happens to the sequence if the common difference changes to +1+1?
  5. How does the formula for the nn-th term differ for a geometric sequence?

Tip: Always verify the common difference before applying the arithmetic sequence formula.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Linear Relationships

Formulas

n-th term of an arithmetic sequence: a_n = a_1 + (n-1)d

Theorems

Arithmetic Sequence Formula

Suitable Grade Level

Grades 8-10