A set of 22 tuning forks is arranged in a series of increasing frequencies. If each fork gives 5 beats per second with the preceding one and last one sounds with the octave of the first, then find the frequencies of the first and the last forks.

Explanation

To solve the problem of finding the frequencies of the first and last tuning forks in a series of 22 tuning forks, we can follow these steps:

### Step 1: Define the frequency of the first tuning fork
Let the frequency of the first tuning fork be denoted as \( \nu \).

### Step 2: Determine the frequency of the subsequent tuning forks
Since each tuning fork gives 5 beats per second with the preceding one, we can express the frequencies of the tuning forks as follows:
- The frequency of the 2nd tuning fork: \( \nu + 5 \)
...