Math Problem Statement
- Find the specified term of the following
a) Identify the 7th term of the sequence: 4, 20, 100, ...
Solution
The given sequence is:
We notice that each term is multiplying by 5, so this could be a geometric sequence. Let’s verify that.
To confirm:
Hence, this is indeed a geometric sequence with the first term and the common ratio .
The general formula for the -th term of a geometric sequence is:
Where:
- is the -th term,
- is the first term,
- is the common ratio, and
- is the position of the term.
Now, to find the 7th term:
Let’s compute :
Now calculate the 7th term:
Thus, the 7th term is:
Would you like more details or have any questions?
Here are 5 related questions to explore:
- What is the 10th term of this geometric sequence?
- Can you derive the formula for the sum of the first terms of a geometric sequence?
- How does changing the common ratio affect the growth of a geometric sequence?
- What happens if the common ratio is a fraction between 0 and 1?
- How do geometric sequences compare to arithmetic sequences in terms of growth?
Tip: Always check for the common ratio or difference when identifying a sequence type—geometric or arithmetic.
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Math Problem Analysis
Mathematical Concepts
Geometric Sequences
Exponents
Formulas
T_n = a * r^(n-1)
Exponential Growth Formula
Theorems
Geometric Sequence Term Formula
Suitable Grade Level
Grades 9-11
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