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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.

 Jun 28, 2020
edited by awnrs  Jun 28, 2020
 #1
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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.

 Jun 28, 2020
edited by Guest  Jun 28, 2020

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