Using inductive reasoning

what is the nth number in the following sequence let's see the first term here is a six so over here I'll put the term so this is the number this is the number I'll just write numb there that's the number and this is the term this is the term so the first term here is a six that looks like we add 3 to that to get to a 9 well maybe there's some other pattern here so that's the second term is 9 then they go from 9 to 12 it looks like we add 3 again so we keep adding 3 so the third term is 12 the fourth term is 15 and we need to think of a general expression that will give us the value of the nth term the nth number in the following sequence so let's think a little bit about it we know that we're incrementing by 3 every time and we're starting at 6 so let's write these in terms of multiples of 3 since we know that that's the increment level this is this first term right here is 3 times 2 the second term right here is 3 times 3 this third term is 3 times 4 and so it looks like it's 3 times 1 more than the actual term you are dealing with right here if you take your term you add 1 and then multiply that by 3 you get 6 take your term add 1 then multiply it by 3 take your term add 1 you get 4 then multiply by 3 take your term add 1 which would be 5 and then multiplied by 3 you get 15 so it looks like anytime so if you have your nth term so if you go all the way out here to your nth term the value here would be you'd add 1 to it so you'd have n plus 1 and then you would multiply that by 3 so the nth term is 3 times n plus 1 or if you wanted to distribute out the 3 it would be 3 and plus 3 and just make sure that works for all of them the first term 3 times 1 is 3 plus 3 that works that's 6 the second term 3 times 2 plus 3 is 9 so it works for all of these terms so that is the instrument have to assumed that this pattern continues