Math Problem Statement
Write the formula for the nth term of the given arithmetic sequence
Solution
The image shows two arithmetic sequences:
- Sequence 1:
- Sequence 2:
Finding the nth term for both sequences:
1. Sequence 1:
This is an arithmetic sequence where the first term and the common difference . The general formula for the -th term of an arithmetic sequence is:
Substituting the values:
So, the nth term of the first sequence is:
2. Sequence 2:
This is also an arithmetic sequence, where the first term and the common difference is:
Using the general formula again:
Substituting the values:
Simplifying:
So, the nth term of the second sequence is:
Would you like further details or have any questions?
Here are five related questions:
- How do we determine the common difference in an arithmetic sequence?
- What is the relationship between the first term and the common difference in a sequence?
- How can you find the sum of the first terms of an arithmetic sequence?
- What is the nth term formula for a geometric sequence?
- How can you extend an arithmetic sequence beyond the 10th term?
Tip: To identify an arithmetic sequence, look for a constant difference between consecutive terms.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Algebra
Formulas
nth term of an arithmetic sequence: a_n = a_1 + (n - 1) d
Common difference: d = a_2 - a_1
Theorems
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Suitable Grade Level
Grades 8-10