1. No. This is because the system does not go up equally every time. There is no common difference
2. Yes. The common difference is 12 and it goes up by that much every single number.
3. The common difference is <u>3</u>. This is because they all have a common difference and it increases by 3.
4. The common difference is -<u>6</u>. This is because every time the number goes down, it has a common difference of -6. The distance from each ascending or descending number in this pattern is 6, but it descends by default, so it would be negative.
5. The common difference is -<u>10</u>, and the next three terms are <u>-20</u>, <u>-30</u>, and <u>-40</u>. The common difference is -10 because the distance from each ascending or descending number is 10, but it descends by itself versus ascending, making the difference negative. The last three numbers are -20, -30, and -40 because you subtract 10 each time.
6. The common difference is 2 and the last 3 numbers are 92, 90, and 88. I think you get how this goes now.
7. Recursive formula: a1=a2-5 .Explicit formula: <em>f</em>(<em>n</em>)=12-5(<em>n</em>-1) 20th term: -83: I seriously do not want to have to explain this. The recursive formula shows term 1 is equal to term 2 plus the common difference. The explicit formula shows the first term, the common difference, and one less than the number term. The 20th term is me just taking away 5 over and over and over again.
8. recursive formula: a1=a2+3 . Explicit formula: f(n)=1+3(n-1) 32nd term: 94
This was really hard to explain. The recursive formula shows term 1 is equal to term 2 plus the common difference. The explicit formula shows the first term, the common difference, and one less than the number term. The 32nd term is me just adding 3 over and over and over again.
