Math Problem Statement
What is a formula for the nth term of the given sequence?
−11,−7,−3...
Solution
To find the formula for the th term of the given sequence , we first need to determine the pattern or rule that defines the sequence. This sequence appears to be arithmetic, where the difference between consecutive terms is constant.
Step-by-Step Solution
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Identify the common difference:
To confirm that the sequence is arithmetic, calculate the difference between consecutive terms:
The common difference is .
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Find the first term:
The first term of the sequence is .
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Use the formula for the nth term of an arithmetic sequence:
The formula for the nth term of an arithmetic sequence is given by:
Here:
- (the first term)
- (the common difference)
-
Substitute the values into the formula:
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Simplify the formula:
Final Formula
The formula for the th term of the sequence is:
This formula allows you to find any term in the sequence by substituting the value of .
Would you like more details or have any questions?
Here are 5 related questions to expand on this topic:
- What is the formula for the sum of the first terms of an arithmetic sequence?
- How do you find the common difference in an arithmetic sequence if it is not given directly?
- Can you explain the difference between arithmetic and geometric sequences?
- How would you determine the 10th term of this sequence using the formula ?
- What changes in the formula if the common difference is changed to ?
Tip: Always double-check the common difference in a sequence to confirm whether it is arithmetic or geometric.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Formulas
Arithmetic sequence nth term formula
Theorems
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Suitable Grade Level
Grades 7-9
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