Math Problem Statement
If a, start subscript, 1, end subscript, equals, 3a1=3 and a, start subscript, n, end subscript, equals, 2, a, start subscript, n, minus, 1, end subscriptan=2an−1 then find the value of a, start subscript, 6, end subscripta6
Solution
Given the recursive sequence defined by:
We need to find the value of .
Let's calculate each term up to step by step:
- Finding :
- Finding :
- Finding :
- Finding :
- Finding :
So, the value of is:
Would you like more details or have any questions about this solution?
Here are 5 related questions to explore:
- What is the value of in this sequence?
- Can you derive a general formula for based on the given recursive relation?
- How does the sequence change if the initial value is different?
- What type of sequence is this, and what are its general properties?
- How would the sequence be affected if the multiplication factor in the recursive relation was 3 instead of 2?
Tip: For geometric sequences, the nth term can often be expressed directly using the initial term and the common ratio raised to a power.
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Math Problem Analysis
Mathematical Concepts
Recursive sequences
Formulas
-
Theorems
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Suitable Grade Level
Grades 10-12
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