Answer: 1) common difference: 9 | explicit form: 1 + 9n | Nth term: [tex]a_{12}=109[/tex]
2) common difference: -5 | explicit form: 20 - 5n | Nth term: [tex]a_{10}=-30[/tex]
Step-by-step explanation:
The "common difference" is what you add each and every time in an arithmetic sequence. #1 goes up by 9, and #2 goes down by 5 (which we can write as having a negative 5 common difference)
The explicit form can take two forms. It's usually [tex]a_{1}-d(n-1)[/tex] with [tex]a_{1}[/tex] being the first term, d being the common difference and n being the index number in the sequence (the first term has index number 1, the second term has index number 2, etc). For the explicit forms I gave, I distributed d and simplified it
Ex: 1) 10 + 9(n-1) = 10 + 9n - 9 = 1 + 9n
Once you have the explicit form, you can just plug in the index number they're asking for. Since it's asking for [tex]a_{12}[/tex] you only have to put 12 into your explicit formula
Ex: 1) 1 + 9n -> 1 + 9(12) = 1 + 108 = 109
Feel free to try to get the values for #2 on your own, the values are in the answer at the top
