Answered

Tuklasin ang mundo ng kaalaman at mga sagot mula sa komunidad sa IDNStudy.com. Ang aming komunidad ay nagbibigay ng eksaktong sagot upang matulungan kang maunawaan at malutas ang anumang problema.

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.

Ang iyong presensya ay mahalaga sa amin. Patuloy na magbahagi ng iyong karanasan at kaalaman. Sama-sama tayong magtutulungan upang makamit ang mas mataas na antas ng karunungan. Ang IDNStudy.com ay laging nandito upang tumulong sa iyo. Bumalik ka palagi para sa mga sagot sa iyong mga katanungan.