In a harmonic progression, if the first term is a and the second term is b, what is the formula for the nth term?
Practice Questions
1 question
Q1
In a harmonic progression, if the first term is a and the second term is b, what is the formula for the nth term?
1/(1/n + 1/a)
1/(1/n + 1/b)
1/(1/a + 1/b)
1/(1/a - 1/b)
The nth term of a harmonic progression can be expressed as 1/(1/a + (n-1)d) where d is the common difference of the corresponding arithmetic progression.
Questions & Step-by-step Solutions
1 item
Q
Q: In a harmonic progression, if the first term is a and the second term is b, what is the formula for the nth term?
Solution: The nth term of a harmonic progression can be expressed as 1/(1/a + (n-1)d) where d is the common difference of the corresponding arithmetic progression.
Steps: 6
Step 1: Understand that a harmonic progression (HP) is a sequence of numbers where the reciprocals of the terms form an arithmetic progression (AP).
Step 2: Identify the first term of the HP as 'a' and the second term as 'b'.
Step 3: Find the reciprocals of the first two terms: 1/a and 1/b.
Step 4: Calculate the common difference 'd' of the corresponding arithmetic progression (AP) using the formula: d = (1/b) - (1/a).
Step 5: The nth term of the HP can be expressed in terms of the first term and the common difference: nth term = 1/(1/a + (n-1)d).
Step 6: Substitute 'd' into the formula to get the final expression for the nth term of the harmonic progression.
