Math Problem Statement
Find the first three terms of the sequence defined by a_n = 10(2)^n, where n represents the position of a term in the sequence. Start with n = 1.
Solution
The given sequence is defined as:
We are asked to find the first three terms of the sequence starting with .
Step-by-step calculation:
-
For :
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For :
-
For :
Final Answer:
The first three terms of the sequence are:
Would you like further details or have any other questions? Here are some related questions you might explore:
- What is the 5th term of this sequence?
- How does the sequence grow as increases?
- Can this sequence be classified as arithmetic or geometric?
- What would happen to the sequence if the base were changed from 2 to another number?
- How could you express the nth term using logarithms?
Tip: Always check the behavior of a sequence for small values of to understand its growth or pattern.
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Math Problem Analysis
Mathematical Concepts
Sequences
Exponential Growth
Formulas
a_n = 10(2)^n
Theorems
None
Suitable Grade Level
Grades 7-9