Math Problem Statement

The first term of a sequence is 12

The term-to-term rule is -3

What is the 5th term of this sequence?

Solution

This sequence follows a term-to-term rule of subtracting 3 from each term.

Given:

  • The first term (T1T_1) is 12.
  • The term-to-term rule is to subtract 3 from the previous term.

Now, calculate the next four terms:

T2=123=9T_2 = 12 - 3 = 9 T3=93=6T_3 = 9 - 3 = 6 T4=63=3T_4 = 6 - 3 = 3 T5=33=0T_5 = 3 - 3 = 0

Thus, the 5th term of the sequence is 0.

Would you like further details or clarification?

Here are 5 related questions to explore:

  1. What is the 10th term of this sequence?
  2. How many terms would it take for the sequence to reach a negative value?
  3. If the term-to-term rule was +3+3 instead of 3-3, what would the 5th term be?
  4. How can this sequence be expressed as an arithmetic sequence formula?
  5. What is the sum of the first 5 terms in this sequence?

Tip: The difference between consecutive terms in a sequence is called the "common difference" in an arithmetic sequence.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Subtraction

Formulas

Arithmetic Sequence: T_n = T_1 + (n-1) * d

Theorems

Common Difference in Arithmetic Sequences

Suitable Grade Level

Grades 6-8