Math Problem Statement

Find the 13th term of the arithmetic sequence: 1, 9, 17, 25, 33, ...

Solution

The image shows a question asking to find the 13th term of the sequence:

1, 9, 17, 25, 33, ...

This is an arithmetic sequence where the first term a1=1a_1 = 1 and the common difference d=8d = 8 (since 91=89 - 1 = 8).

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

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

Now let's find the 13th term (n=13n = 13):

a13=1+(131)8a_{13} = 1 + (13 - 1) \cdot 8 a13=1+128a_{13} = 1 + 12 \cdot 8 a13=1+96=97a_{13} = 1 + 96 = 97

Thus, the 13th term is 97\boxed{97}.

Would you like more details or explanations?

Here are 5 related questions to expand on this concept:

  1. What is the 20th term of this arithmetic sequence?
  2. How do you find the sum of the first 13 terms of this sequence?
  3. What happens if the common difference changes in an arithmetic sequence?
  4. Can you express this arithmetic sequence in a recursive form?
  5. How do arithmetic sequences apply in real-world situations?

Tip: Always check the common difference in arithmetic sequences to ensure you're using the correct pattern for finding terms!

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Algebra

Formulas

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

Theorems

Arithmetic Sequence Theorem

Suitable Grade Level

Grades 6-8