If the nth term of a harmonic progression is given by 1/(1/n + 1/a), what does 'a' represent?

1 question

1 item

Q: If the nth term of a harmonic progression is given by 1/(1/n + 1/a), what does 'a' represent?

Solution: 'a' represents the first term of the harmonic progression in the formula for the nth term.

Steps: 5

Step 1: Understand what a harmonic progression (HP) is. A harmonic progression is a sequence of numbers where the reciprocals of the numbers form an arithmetic progression (AP).
Step 2: Recall the formula for the nth term of a harmonic progression. The nth term can be expressed as 1/(1/n + 1/a).
Step 3: Break down the formula. In the formula 1/(1/n + 1/a), '1/n' represents the reciprocal of the nth term of the HP.
Step 4: Identify what '1/a' represents. Since 'a' is in the formula, it indicates the reciprocal of the first term of the harmonic progression.
Step 5: Conclude that 'a' is the first term of the harmonic progression because it is the value that, when taken as a reciprocal, contributes to the nth term.