Math Problem Statement
A sequence of numbers is written in such a way that is number is greater than the receiving number by three starting the sequence from -2, the 10th number of the sequence is
Solution
We are given a sequence where each number is 3 greater than the previous one, and the sequence starts at -2. This is an arithmetic sequence.
Formula for the -th term of an arithmetic sequence:
Where:
- is the -th term,
- (the first term),
- (the common difference),
- is the term number.
We are asked to find the 10th term, so .
Substituting into the formula:
Thus, the 10th number of the sequence is 25.
Would you like more details or have any questions?
Here are 5 related questions:
- What would the 20th term of this sequence be?
- How do you find the sum of the first 10 terms of an arithmetic sequence?
- Can you describe how the common difference affects the growth of the sequence?
- What is the general formula to find any term in an arithmetic sequence?
- How can we identify whether a sequence is arithmetic or not?
Tip: For any arithmetic sequence, the difference between consecutive terms remains constant, making it easy to predict future values.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Linear Progressions
Formulas
nth term of an arithmetic sequence: a_n = a_1 + (n - 1) * d
Theorems
Arithmetic sequence theorem
Suitable Grade Level
Grades 6-8
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