Math Problem Statement

On the arithmetic sequence 9, 14, 19, 24, what is the 71st term?

Solution

The given arithmetic sequence is 9,14,19,24,9, 14, 19, 24, \ldots.

In an arithmetic sequence, the general form of the nn-th term is:

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

Where:

  • ana_n is the nn-th term,
  • a1a_1 is the first term,
  • dd is the common difference,
  • nn is the position of the term.

From the sequence:

  • The first term a1=9a_1 = 9,
  • The common difference d=149=5d = 14 - 9 = 5.

To find the 71st term (a71a_{71}):

a71=9+(711)5a_{71} = 9 + (71 - 1) \cdot 5 a71=9+705a_{71} = 9 + 70 \cdot 5 a71=9+350=359a_{71} = 9 + 350 = 359

Thus, the 71st term of the sequence is 359359.

Would you like further details or have any questions?


Here are 5 related questions:

  1. What is the 100th term of this sequence?
  2. How can you find the sum of the first 71 terms of this arithmetic sequence?
  3. What would the 50th term be if the common difference was 3 instead of 5?
  4. How can you determine the common difference if only two terms are known?
  5. What is the general formula for the sum of an arithmetic sequence?

Tip: The common difference in an arithmetic sequence can be found by subtracting any two consecutive terms.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequence
Sequences and Series

Formulas

a_n = a_1 + (n - 1) * d

Theorems

General formula for the nth term of an arithmetic sequence

Suitable Grade Level

Grades 6-8