How many positive integers less than 2020 aren’t divisible by 2, 3, or 5?

The arithmetic mean of 23, 16, 30, 33 and two other numbers that differ by 2 is 21. If the smallest of these 6 numbers is discarded, find the arithmetic mean of the remaining 5 numbers.

The fifth term of an arithmetic sequence is -18, and the sum of the first 32 terms is 1448. Find the ninth term.

awnrs Jun 28, 2020

#1**0 **

How many positive integers less than 2020 **aren’t divisible by 2, 3, or 5?**

a=0;b=0;c=0;d=0;p=0; cycle:n=a*1000+b*100+c*10+d;if(n%2==1 and n%3!=0 and n%5!=0 and n<=2020, goto loop, goto next); loop:printn,", ",;p=p+1; next:d++;if(d<10, goto cycle, 0);d=0;c++;if(c<10, goto cycle, 0);d=0;c=0;b++;if(b<10, goto cycle,0);b=0;c=0;d=0;a++;if(a<3, goto cycle,0);print"Total = ",p

**OUTPUT = 538 - numbers that are NOT divisible by 2 or by 3 or by 5.**

The fifth term of an arithmetic sequence is -18, and the sum of the first 32 terms is 1448. Find the ninth term.

- 18 =[F + 4D], 1448 =32/2 * [2*F + 31D], solve for F, D

F = - 40 - This is the first term

D =11/2 =5.5 - This is the common difference

**- 40 + [8 x 5.5] = 4 - This is the 9th term.**

Guest Jun 28, 2020

edited by
Guest
Jun 28, 2020