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Sagot :
Answer:
The number of terms in the arithmetic progression is 5.
Step-by-step explanation:
1. Given Information:
- The first term of the arithmetic progression (AP) is 3.
- The fifth term of the AP is 9.
2. Finding the Common Difference:
- We use the formula for the \( n \)-th term of an AP: \( a_n = a + (n-1)d \), where \( a \) is the first term, \( d \) is the common difference, and \( n \) is the term number.
- Since \( a = 3 \) and \( a_5 = 9 \), we substitute these values into the formula to find \( d \).
- \( a_5 = a + 4d \)
- \( 9 = 3 + 4d \)
- Solving for \( d \), we get \( d = \frac{9 - 3}{4} = \frac{6}{4} = 1.5 \).
3. Finding the Number of Terms:
- We want to find the number of terms in the progression. Let's denote it as \( n \).
- We use the formula for the \( n \)-th term again: \( a_n = a + (n-1)d \).
- Since we know the last term of the progression (which we'll assume is 9), we set \( a_n = 9 \) and solve for \( n \).
- \( 9 = 3 + (n-1) \times 1.5 \)
- Solving for \( n \), we get \( n = 5 \).
4. Conclusion:
- The number of terms in the arithmetic progression is 5.
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