Math Problem Statement

A sequence starts with $122$, and each term decreases by $5$. What is the fourth term of the sequence?

Solution

The given sequence starts with 122122 and each term decreases by 55. This is an arithmetic sequence with the first term a=122a = 122 and a common difference d=5d = -5.

To find the fourth term, we use the formula for the nn-th term of an arithmetic sequence:

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

For the fourth term (n=4n = 4):

a4=122+(41)(5)a_4 = 122 + (4 - 1) \cdot (-5)

a4=122+3(5)a_4 = 122 + 3 \cdot (-5)

a4=12215a_4 = 122 - 15

a4=107a_4 = 107

So, the fourth term of the sequence is 107\boxed{107}.

Would you like more details or have any questions?

Here are some related questions to consider:

  1. What is the 10th term of this sequence?
  2. How many terms are there in this sequence until it reaches zero or below?
  3. What is the sum of the first 10 terms of this sequence?
  4. What is the general formula for the nn-th term of this sequence?
  5. How does the sequence behave as nn becomes very large?

Tip: In an arithmetic sequence, the difference between consecutive terms is always constant.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences

Formulas

Arithmetic sequence nth term formula

Theorems

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Suitable Grade Level

Grades 7-9