Math Problem Statement
Solution
The problem states that the terms in the sequence increase by the same number each time, making it an arithmetic sequence. The known terms are:
- Term 1 = 3
- Term 5 = 19
Let's determine the common difference, , and use it to find Term 6.
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In an arithmetic sequence, each term can be expressed as:
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We know: Substituting the values:
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Solving for :
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Now, we use this common difference to find Term 6:
Therefore, the value of Term 6 is 23.
Would you like further details, or have any questions?
Here are some related questions:
- How would you find the 10th term in this sequence?
- What is the sum of the first six terms in this sequence?
- How do you verify that this is indeed an arithmetic sequence?
- What is the general formula for the nth term in this sequence?
- If the first term was different, how would that affect the sequence?
Tip: In arithmetic sequences, understanding the common difference helps in predicting subsequent terms easily.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Algebra
Formulas
Arithmetic sequence formula: T_n = T_1 + (n - 1) * d
Theorems
Arithmetic Sequence Definition
Suitable Grade Level
Grades 6-8
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