Math Problem Statement

The first term of an arithmetic sequence is 5, and the common difference of the sequence is 2. What is the eighth term of the sequence?

Solution

This is a problem involving an arithmetic sequence. The formula for the nth term of an arithmetic sequence is:

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

Where:

  • ana_n is the nth term.
  • a1a_1 is the first term of the sequence.
  • dd is the common difference.
  • nn is the term number.

Given:

  • The first term a1=5a_1 = 5,
  • The common difference d=2d = 2,
  • The goal is to find the 8th term (i.e., n=8n = 8).

Now, substitute the values into the formula:

a8=5+(81)2=5+72=5+14=19a_8 = 5 + (8 - 1) \cdot 2 = 5 + 7 \cdot 2 = 5 + 14 = 19

Thus, the 8th term of the sequence is 19, which corresponds to option A.

Would you like further explanation or have any questions? Here are some related questions you might find useful:

  1. How can you derive the general formula for an arithmetic sequence?
  2. What happens if the common difference is negative?
  3. How do you determine the sum of the first nn terms in an arithmetic sequence?
  4. How is an arithmetic sequence different from a geometric sequence?
  5. How can you use an arithmetic sequence in real-world applications?

Tip: Always remember to double-check the term number you're solving for in the sequence formula to avoid errors.

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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

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Suitable Grade Level

Grades 6-8