Math Problem Statement
how many terms are in the sequence 4,7,10,...61?
Solution
To determine the number of terms in the sequence , we can recognize this as an arithmetic sequence where:
- The first term .
- The common difference .
The general formula for the -th term of an arithmetic sequence is:
We need to find when the last term . Plugging in the values:
Simplify the equation:
Now, divide both sides by 3:
So,
Therefore, there are 20 terms in the sequence.
Would you like a detailed explanation of any step? Here are some related questions:
- How do you find the common difference in an arithmetic sequence?
- What is the formula for the sum of an arithmetic sequence?
- How do you find the -th term of an arithmetic sequence?
- Can this method be used for sequences with different patterns?
- What changes if the sequence is geometric instead of arithmetic?
Tip: Always identify the common difference or ratio when dealing with sequences—it’s the key to finding missing terms or sums!
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequence
Sequences and Series
Formulas
nth term formula for arithmetic sequence: a_n = a + (n - 1) * d
Theorems
Arithmetic Sequence Formula
Suitable Grade Level
Grades 8-10
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