Math Problem Statement
Solution
The image shows a function machine that produces a sequence, where the position in the sequence is first multiplied by 4, and then 3 is added. This is a linear transformation, and we can write it as:
To find the 20th term, we substitute the position value (20) into this equation:
So, the 20th term in the sequence is 83.
Would you like more details on how this works or have any further questions? Here are some related questions for deeper understanding:
- How would the sequence change if the multiplier was different, like 5 instead of 4?
- What if we added a larger number, say 10, instead of 3? How would that affect the terms?
- How would you find the nth term in a sequence like this, where the operation is a linear transformation?
- What is the general form for any arithmetic sequence that uses multiplication and addition?
- How can we graph this sequence, and what would its graph look like?
Tip: A quick way to solve for terms in a sequence like this is to use the formula derived from the function machine directly for any position, rather than calculating each term step by step.
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Math Problem Analysis
Mathematical Concepts
Sequences
Linear Transformations
Arithmetic Sequences
Formulas
Term = (Position × 4) + 3
Theorems
Linear Transformation Theorem
Suitable Grade Level
Grades 5-7