moena1:

what is the 89th odd positive integer

sillybilly123:

For evens this would be easy, right?! So, for $$k = 1,2,3,...$$, the even no's are 2k. Ie they are: $$2 * 1 = 2, 2* 2= 4, 2*3 = 6,....$$. So, for example, 21st even number is $$2 * 21 = 42$$. For the odds, subtract 1, ie for $$k = 1,2,3,...$$, the odds are 2k-1. so they are: $$(2 * 1) - 1 = 1, (2* 2) - 1 = 3, (2*3) - 1 = 5,....$$ Then, if you're convinced by that, the 89th odd occurs at k = 89 and is $$(2 *89) - 1 = \dots \dots$$ Idea is really important, say, for series notation.