Answer:
1) n
2) 2n
3) 2n+1
4) 3n-2
5) -n
Step-by-step explanation:
To write a generalized statement for a pattern using n, we multiply n by the common difference between each term. We add the term number <em>before</em> the first term to this.
1) 1, 2, 3...
For the first question, the common difference is 1 because each term increases by 1. Multiply n by 1.
1n
To find the term number <em>before</em> the first term, we subtract 1 from the first term.
1-1=0
Therefore, our general statement is 1n+0, or just n.
2) 2, 4, 6...
The common difference is 2 because we add 2 each time. Multiply n by 2.
2n
The term number <em>before</em> the first term is equal to the first term - the common difference.
2-2=0
Therefore, our general statement is 2n+0, or just 2n.
3) 3, 5, 7...
The common difference is 2 because we add 2 each time. Multiply n by 2.
2n
The term number before the first term is equal to the first term - the common difference.
3-2=1
Therefore, our general statement is 2n+1.
4) 1, 4, 7, 10...
The common difference is 3 because we add 3 each time. Multiply n by 3.
3n
The term number before the first term is equal to the first term - the common difference.
1-3=-2
Therefore, our general statement is 3n+(-2), or 3n-2.
5) -1, -2, -3...
The common difference is -1 because we subtract 1 each time. Multiply n by -1.
-1n
The term number before the first term is equal to the first term - the common difference.
-1-(-1)
= -1+1 (because two negatives make a positive)
= 0
Therefore, our general statement is -1n+0, or just -n.
I hope this helps!
