In a harmonic progression, if the first term is 2 and the second term is 4/3, what is the third term?
Practice Questions
1 question
Q1
In a harmonic progression, if the first term is 2 and the second term is 4/3, what is the third term?
1
3/2
2/3
1/2
In a harmonic progression, the reciprocals of the terms form an arithmetic progression. The reciprocals of the first two terms are 1/2 and 3/4. The common difference is 1/4, so the reciprocal of the third term is 1/2 + 1/4 = 3/4. Therefore, the third term is 1/(3/4) = 4/3.
Questions & Step-by-step Solutions
1 item
Q
Q: In a harmonic progression, if the first term is 2 and the second term is 4/3, what is the third term?
Solution: In a harmonic progression, the reciprocals of the terms form an arithmetic progression. The reciprocals of the first two terms are 1/2 and 3/4. The common difference is 1/4, so the reciprocal of the third term is 1/2 + 1/4 = 3/4. Therefore, the third term is 1/(3/4) = 4/3.
Steps: 7
Step 1: Identify the first term of the harmonic progression, which is 2.
Step 2: Identify the second term of the harmonic progression, which is 4/3.
Step 3: Find the reciprocals of the first two terms. The reciprocal of 2 is 1/2, and the reciprocal of 4/3 is 3/4.
Step 4: Recognize that the reciprocals (1/2 and 3/4) form an arithmetic progression.
Step 5: Calculate the common difference between the two reciprocals. The common difference is 3/4 - 1/2 = 1/4.
Step 6: Add the common difference to the last reciprocal (3/4) to find the reciprocal of the third term. So, 3/4 + 1/4 = 1.
Step 7: The reciprocal of the third term is 1, which means the third term itself is 1/1 = 1.
