Question

how many positive integers less than 220 have a remainder of 3 when divided by 9?

Answer 1

first lets start by listing some of the integers that have a remainder of 3 when divided by 9.
3, 12, 21, 30, 39,...., 219
So we just need to figure out how many numbers are in that list.

Answer 2

All of these numbers are in the form:
9k+3, for k =0, 1, 2, 3, 4....
we can see this because:
9(0)+3 = 3
9(1)+3 = 12
so on and so forth.

Answer 3

Just find the last of the possible ones which is 219, and as stated previously in the form 9k+3, therefore 219=9k+3 , k=24 , hence your answer is 24 integers.

Answer 4

so to figure out how many numbers there are, we solve:
219 = 9k+3
216 = 9k
24 = k
so there are 25 numbers on the list.

Answer 5

The equation will be 9A+3
Put the value of A = 0,1,2,3....24
Get the series ..
Apply A.P get n=?

Answer 6

25

Answer 7

its 25 numbers, because we started at k = 0

Answer 8

My apologies, 3 is also included , so it is 25 integers