Math Problem Statement
an-d form of a_n=53+(n-1)*3
Solution
The sequence is in arithmetic sequence form where:
- (the first term)
- (the common difference)
To express this in the general form of , it simplifies as follows:
Distribute to :
Simplify the constants:
So, the simplified form of the sequence is:
Questions for Deeper Exploration:
- What is the 10th term of the sequence?
- How do you find the sum of the first 20 terms of this sequence?
- If the sequence were geometric instead, how would the formula change?
- What is the -th term if the first term were ?
- Can you find the inverse function of this sequence, i.e., solving for in terms of ?
Tip:
In arithmetic sequences, the difference determines the "rate of change" between consecutive terms, so always look for patterns in differences to verify your formula.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Linear Algebra Equations
Formulas
General form of an arithmetic sequence: a_n = a_1 + (n-1)d
Simplified linear form: a_n = 3n + 50
Theorems
Properties of Arithmetic Sequences
Suitable Grade Level
Grades 8-10