Find total number of integers.
\(a_1=10,a_n=60,d=1 \\a_n=a_1+(n-1)d \\60=10+(n-1)1 \
-1=50 \
=51\)
Find how many integers is divisible by 2.
\(a_1=10,a_n=60,d=2
\\a_n=a_1+(n-1)d
\\60=10+(n-1)2
\\2(n-1)=50
\
-1=25
\
=26\)
Eliminate even numbers.
11, 13, 15,..., 57, 59
This array contains 51 - 26 = 25 numbers.
Eliminate numbers before the first number divisible by 3 and after the last number divisible by 3.
15, 17, 19,..., 55, 57
This array contains 25 - 3 = 22 numbers.
Now we should eliminate numbers divisible by 3: 15, 21, 27...
\(a_1=15,a_n=57,d=6,n=?
\\a_n=a_1+(n-1)d
\\57=15+(n-1)6
\\6(n-1)=42
\
-1=7
\
=8\)
There are 8 such numbers.
Therefore, there are 25 - 8 = 17 numbers that can be evenly divided by neither 2 nor 3