Using an arithmetic sequence, it is found that you would need to do 32 subtractions
In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem:
Then:
[tex]a_n = a_1 + (n - 1)d[/tex]
[tex]a_n = 100 - 3(n - 1)[/tex]
[tex]a_n = 103 - 3n[/tex]
To get a single-digit number, we need that:
[tex]a_n \leq 9[/tex]
Hence, solving the inequality:
[tex]103 - 3n \leq 9[/tex]
[tex]-3n \leq -94[/tex]
[tex]3n \geq 94[/tex]
[tex]n \geq \frac{94}{3}[/tex]
[tex]n \geq 31.3[/tex]
Rounding up, 32 subtractions need to be done.
A similar problem is given at https://brainly.com/question/23842987
