Math Problem Statement

An arithmetic sequence is represented by the function f(n) = 3 + 2n. What is the fifth term of the sequence?

Solution

The given arithmetic sequence is represented by the function:

f(n)=3+2nf(n) = 3 + 2n

We are asked to find the fifth term of the sequence, which corresponds to n=5n = 5.

To calculate f(5)f(5), we substitute n=5n = 5 into the formula:

f(5)=3+2(5)=3+10=13f(5) = 3 + 2(5) = 3 + 10 = 13

Therefore, the fifth term of the sequence is 13 (Option B).

Would you like further details or have any questions?

Here are five related questions for further practice:

  1. What is the first term of the sequence?
  2. What is the common difference in this arithmetic sequence?
  3. How do you find the 10th term of this sequence?
  4. If the sequence continues, what is the 20th term?
  5. How can you generalize an arithmetic sequence?

Tip: In arithmetic sequences, the difference between consecutive terms is constant. This difference is called the common difference and plays a key role in the formula.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Algebra

Formulas

f(n) = a + (n-1) * d
f(n) = 3 + 2n

Theorems

Arithmetic sequence formula

Suitable Grade Level

Grades 6-8