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The first term of an ap is 3 and the fifth term is 9,find the number of term in the ptogressin

Sagot :

Kiaisabombidn

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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